“me doing something” or “my doing something”?

Question

Tell me please which one of the following sentences is correct.

I cannot explain me having hired him.

I cannot explain my having hired him.

Answer 1

I cannot explain my having hired him. (correct)

Explanation

In this sentence, "having" is a gerund (a gerund can take the place of a noun) and so "my having" is correct.

Here is another example:

The Special Verbs That Are Also Nouns - Gerunds in English

"I never believe nor disbelieve. If you will excuse my speaking frankly, I mean to observe you closely, and to decide for myself." (Wilkie Collins, Percy and the Prophet, 1877)

https://www.thoughtco.com/gerund-in-grammar-1690897