mine
In French, the word 'le mien' is used to express possession in a masculine context. It translates to 'mine' in English and is used in the same way. For example, if you wanted to say 'this book is mine', you would say 'ce livre est le mien'.
This is mine, not yours.
In this sentence, 'le mien' is used to indicate possession. The speaker asserts that something belongs to them (it is 'mine') and not to the listener (not 'yours').
I forgot mine at home.
In this case, 'le mien' is used to denote an object that was forgotten at home. The specific object is implicit and can be understood from the context of the conversation.
Your hat is nice, but I prefer mine.
Here, 'le mien' is used to express a preference. The speaker likes their own hat (le mien) more than the hat of the person they are speaking to.