Can I start a phrase like this: "your green eyes are beautiful" or "His/her green eyes are beautiful" Thanks for reply.
Yes, it is perfectly OK to start a sentence with a pronoun. Indeed, I is one of the most common words to start a sentence. Your is not actually a pronoun: it is a determiner. The difference is that a pronoun replaces a noun:
the book is on the table -> it is on the table
whereas a determiner goes before a noun to say which one you are talking about:
the book is on the table -> my book is on the table
Compare that with mine which is a relative pronoun, and you will see that the noun book disappears:
the book is on the table -> mine is on the table
Here is an NGram showing that both pronouns and determiners are very common at the start of a sentence.