Originally Posted by I

1 Michael and David disagree about Michael puttting up his posters

2 David hitting mary is the worst scene of the show.

1.So we can change "put up" to "putting up" "hit" to "hitting"
to make the sentences "Michael put up his posters" "David hit mary" to be noun?

Originally Posted by Mikenewyork

No, we can't. In both of these cases, the -ing verbh form is a verbal. A verbal is a verb form used not as a verb, but as another part of speech. In both of yoyur examples, the -ing verbal is a present participle, used as an adjective. Because it retains verb-like qualities, the participle can take verb modifiers and a direct object. In the first, "putting up his posters" is a participial phrase describing an action of Michael; in the second, "hitting Mary" is a participial phrase describing an action of David.
Another -ing verbal is called a gerund. A gerund is a verbal used as a noun. We'll get to that later.