Depending on the grammar guide or grammar expert that you consult, you may get different advice. Many teachers will tell you that "I don't mind him watching TV" is wrong and that the correct way to say/write it is "I don't mind his watching TV". They claim that in this sentence the word "watching" is a gerund, which is a type of noun, and that object pronouns such as "him" can't modify nouns, only possessive pronouns can do that. However, outside of literature and formal writing it is more common to say "I don't mind him watching TV", and many people will consider this to sound more natural and normal, and they will consider "his watching" to sound more formal or old-fashioned. My advice: in formal or academic writing try to avoid saying something like "I don't mind him watching TV", and in casual writing or speech do as you wish.

Hi, Jane. The example sentence would be most correct in the following ways: a) "I don't mind that he watches TV" (in other words, he watches TV generally as a rule) and b) "I don't mind that he is watching TV" (in other words, he is watching TV right now). We wouldn't use "him" in the example sentence. I hope this is helpful.

In the full illustration, " I don't mind him If he is watching TV." Meanwhile, It would better to say "I don't mind him watching TV" HIM is the exact world put it inside.

It would be "I don't mind him watching TV". The other one sounds quite awkward.