Alright lets assume Planet X is real.

Let's assume it has an inner system orbit that brings it just within the orbit of the Asteroid Belt and so far out no one can see it every 3600 years (roughly).

First passing would have caused the orbits of Mars, Earth and Venus to elongate slightly, may not have touched Mercury at all. However the Elongation of Venus and Earth's orbit would put tidal stresses on Mercury slowly causing Mercury's orbit to elongate over hundreds of years after its passing.

IF The asteroid belt is indeed a "failed" planet or is the remains of a planet, then we could blame Planet X for the break up of that planet at the first round. We don't need another planet to cause the asteroid belt, the Gravitational tidal effects of Jupiter and Mars has enough influence to prevent a planet from forming at the asteroid belt.

3600 years later PX returns.

The Asteroid Belt would be influenced causing the near and farthest sides (relative to the sun) to PX to spew asteroids in every direction. A "Rain of Fire" would follow about 50 years later on Mars, Earth and Venus. Destabilized orbits of this debris would continue for each orbital return, in as little as three orbits the asteroid belt would cease to exist, in as much as 5 it would be gone.

Mars would be pulled further outward, coming dangerously closer to Jupiter's influence Every 3.5 years as the orbit of Mars beings it to its closest approach henceforth Jupiter would pull it further out from its place.

Earth would be on a slightly increasing elliptical orbit, Jupiter would be affecting Earth's orbit with less force, yet each year as Earth and Jupiter are at closest approach, Earth would swing a tad further out. Venus would be the least affected by Jupiter, and could have stabilized in its elongated orbit.

Mercury would be influenced by Venus and would elongate its orbit to the point where the solar wind of our sun would slow it down each orbit until Mercury would have fallen into the Sun.

3600 years later. Mars would be sweeping the inner edge of the Asteroid Belt, Jupiter's influence pulling Mars ever closer.

Earth would be baking during the 'summer' and freezing during the winter. Its elliptical Orbit would be the main reason for the season as it now skirts Venus's old circular orbit and gets as far as halfway to Mar's old orbit. Life is gone BTW having either froze or burnt.

The Third approach of PX would now cause at least one of the three inner planets to break from its elliptical orbit.

Mar's is the most likely having now reached a height of its orbit to be strongly influenced by PX. It would either be thrown into a spiral "downward" into the sun, or be thrown into an escape orbit tossing the planet out toward the outer solar system, or if conditions are just right PX would capture Mars.

Earth's orbit would have to wait another round. Venus on the other hand being as close as it is to the sun and moving as 'fast' as it does relative to the orbit of PX could be thrown outward or sent into a downward spiral.

Assuming very good luck, the effect for all three planets is minimal thus they only suffer more elongation of their orbits.

A few hundred years later the influence of Jupiter on Mars would cause Mar's to pass the asteroid Belt's orbit (which would have no asteroids since they would have been either thrown further out or sent on a downward spiral, or be collected by the gravity of PX captured as temporary moons before they spiral inward to crash on PX.

Earth now skirts well beyond Mar's initial orbit, its course is more like a comets instead of a planets. Its closest approach to the sun puts it well within the orbit of Venus (as we know Venus's orbit). Venus itself is also following a similar trajectory, coming as close to the sun as Mercury used to.

The fourth passing would indeed be the last passing for the inner planets. Mars would be the first affected, most likely thrown outward, potentially being pulled apart by the gravity tides of PX if not Jupiter. A low probability exists that Mars could be captured by Jupiter or PX.

Earth's orbit would be so elongated that it could either be captured by PX or Jupiter or it would burn up in the sun.
Venus's orbit would bring it too close to the sun, it too would succumb to the solar wind, its orbit decay and it would burn up in the sun.

Within 5 orbits of a near inner solar system object as large as a gas giant would be enough to clean out the terrestrial planets.

Assuming 3600 years per orbit, in as short as 180,000 years the inner solar system would be empty of any planets.

This is how we know that PX as described by such notable individuals as the woman who listens to voices (Nancy Leider) that PX as described by them can not exist.

We have the math to predict exactly what would happen. And further we have discovered planetary systems with large gas planets that describe an orbit as proposed by the PX theory, and all evidence upholds the math and an empty inner system.

All of the "predicted" effects that Nancy and her kin predict of a theoretical inner solar system approaching Gas Giant would not take place. No shifts, not huge tides, not even a single earth quake.

In order for those effects to take place PX would have to come in much further into the solar system (Pass Mars, Closely approaching Earth Orbit).

In this case it would take only 1 orbit to perfectly frell the machinery of the orbits of the planets.

After its initial passing all of the inner planets would be on highly eccentric elliptical orbits. So much so that life would cease to exist here on Earth. The potential of planetary collisions increases with a near certainty that the gravitation of the inner planets would further skew each others orbits. By the second passing Mercury would have long fell into the sun, and the other remaining three would be flung outward, or inward, or be 'smashed' by tidal influences as Jupiter and PX "fight" over the terrestrial planets.