Alternative history: what would happen if Alexander the Great tried to take over china?

He barely reached India. By then his & his army's stamina & spirit were worn out thin. China is still far to east, that they can't hope to attempt it even. I wonder whether they had any awareness even of a country called China then, beyond the vaguest picture.

As the evil genius said in "The Princess Bride": "Don't start a land war in Asia!"

Alexander was a military genius who was able to defeat well trained, well equipped armies and build alliances to enlarge his own army, so it is possible that he would have been able to take on the Chinese armies and win, especially if he had been able to divide and conquer. During his lifetime, China was in its warring states period, so he would not have faced a united Chinese army.

The expansion of Alexander's empire was checked by his premature death, and his troops becoming homesick.

If Alexander had lived longer and continued expanding his empire east, he would still have taken many years to reach China. He would have had to conquer tribes and civilisations along whichever route he chose, build fortresses, and establish systems of taxation in order to keep his armies fed. All these people would have to be effectively subdued and assimilated into his armies. If any of the people he had conquered further west rebelled, they could potentially have cut off his supplies and placed him in a position where he was surrounded by hostile armies on all sides. He would have to be careful to consolidate his power and not stretch his supply lines out too thinly. The Mongols managed to conquer China, Central Asia and parts of Europe and the Middle East, but they ultimately had to divide their empire for administrative purposes.

Alternatively, he COULD have plundered his way across Asia abandoning all his territories in the west in order to conquer China. It's unlikely he would have chosen to do it this way, but if he had been betrayed in the west by a rebellion or coup, he might have ended up stranded in Asia with an army and MIGHT have chosen to go east rather than attempting to reclaim his western empire, but this scenario is pretty unlikely.

What is almost certain is that his empire, had it expanded larger than it did would have collapsed after his death.

It wouldn't have been possible. Already by the time he reached India his men were on the verge of mutiny, as they wanted to go back home. The troops thought their mission complete when Persia was beaten, and didn't want to go farther into Asia. Alexander temporarily regained their support with an impassioned speech but soon a plot against his life showed that his plans (for a universal state and brotherhood of Man) were beyond the comprehension of his followers and his dream could only be fulfilled at great cost.

Under the circumstances, Alexander couldn't have gone all the way to China and conquered it, even if he succeeded in taking over India. The distances were far too great and the task far too daunting. His troops wouldn't have gone half the distance and few if any would've survived had they tried.