I have bike with 2x8 compact chain ring in front 50/34. If I change the 50 to 46 do I need to cut the chain shorter? I know I will adjust the front derailleur lower, right?
Short answer: no.
You would need to check if it needs to be shortened if you used a smaller small chain ring. Or you might need a longer chain if you used a larger large chain ring. Your chain should be long enough to allow the big-big combination, and short enough so in the short-short-combination, your rear derailleur still creates some tension and the chain doesn't slide over other parts than the pulleys.
I know I will adjust the front derailleur lower, right?
Maybe, but not really.
A 50T chainring is 208.8mm in diameter and a 46T is 192.7mm So you might think that the front mech needs to move down by half the difference, which is about 8mm.
However your smaller chainring(s) haven't changed. Thus, if the tail of the FD's cage worked where it was, then it will continue to work without adjustment.
If you were going the other way, from 46T to 50T then you would probably need to raise the front derailleur. But I think you can try it without changes, and this gives an easy path back should you decide to refit the 50T.