I am from the Philippines,when can we say that the father already abandoned the children? Can a 24 and 20 years old children living with there mother can sued the father for abandonment?

You can't abandon 20 and 24 year old children as a parent... because they are adults. And responsible for themselves.

Abandonment can be used for grounds for something else, but isn't something you file for itself.

What is it you really want? Do you want a divorce or are you even married to the father? Your children are adults, so there is no issue of abandonment with reference to them.