He understands that he eats noisily, but he always to forget

He understands that he eats noisily, but he always (to forget) about it.

He understands that he eats noisily, but he always forgets about it.

Здесь always - всегда. forget - глагол не деяния. Поэтому pres simp. Он всегда забывет.

Но если желайте выразить раздражжение:

He understands that he eats noisily, but he is always forgeting about it.

Тут always - постоянно. Постоянно он запамятывает.

У Вас учебник, вероятно, с украинской грамматикой британского языка.