Shouldn't show favour TO him. Although 'shouldn't favour him' is more common. You could say shouldn't favour him over ..(someone else).

Hi Ethan, You wouldn’t really use a preposition in this instance. You could say “The teacher shouldn’t show favor to him,” but people usually say, “The teacher shouldn’t play/have favorites.” You could also say, “The teacher shouldn’t favor him.” Hope that helps.

Since you didn't supply context, it's not clear what you mean. "playing favorites" as mentioned by Heidi would be informal, but I'd be more apt to say (AmE) "Teachers shouldn't show favoritism" "The teacher shouldn't show favoritism towards him"