Hello, Mrtkrdmn, and welcome to the Grammar Exchange!
Think about I am talking to someone and I am saying “Two month ago, I started to study English again and I understand I am good at it”
”I started to study English again and I understood I was good at it”
Which is correct?
Unfortunately, it is ungrammatical in English to use clauses as objects of prepositions. Instead of saying *"Think about I am talking to someone," you could say, "Let's suppose I am talking to someone." Another problem is that "two month" should be "two months," because "month" is a count noun.
As for the use of the present tense ("understand") or the past tense ("understood"), the whole part of the sentence in which the word appears doesn't work very well in coordination with the first half. It would make more sense to use "discovered" (past tense) in the second independent clause:
- I started to study English again, and I discovered I was good at it.
Since both independent clauses have the same subject, you could combine them:
- I started to study English again and discovered I was good at it.