"El nu poate să înțeleagă!"

Translation: He cannot understand!

[Schattenparker]

a înțelege
indicative # subjunctive
eu înțeleg # să înțeleg
tu înțelegi # să înțelegi
el/ea înțelege # să înțeleagă
noi înțelegem # să înțelegem
voi înțelegeți # să înțelegeți
ei/ele înțeleg # să înțeleagă

[MichaelSquire]

"He can not understand" should be accepted as correct answer. Right now it is not.

[Patricia229086]

"He cannot (or can't) understand" means he is incapable. "He can not understand" means he is capable of not understanding if he choses.

[sigmacharding]

Why do we sometimes use the infinitive after "Putea" and other times the subjunctive?

The use of the subjunctive seems a little different from the other romanance languages I have studied. For example here there is no change of subject.

Would it also be correct to say "El nu poate înțeleage"

[potestasity]

Minor nitpick: the infinitive is "a înțelege".
And yes, you can say "El nu poate înțelege."
You can even say "El nu poate a înțelege.", although this form is more awkward and belongs rather to a dramatic context than common speech.
The thing is that the subjunctive is just the most common way of expressing this. Whenever a bunch of languages (e.g. English, French) would use the infinitive with verbs like "can", "want", "wish" etc., Romanian would use the subjunctive:
He can eat. - El poate să mănânce.
He wants to eat. - El vrea să mănânce.
He refuses to eat. - El refuză să mănânce.
He decides to eat. - El decide să mănânce.

[GrantHanha]

"He was not able to understand" marked wrong but I think more correct.

[GrantHanha]

"He is not able to understand" marked correct. Thanks Duo !