Which sentence is correct:
Mine are the red packages on the right
My are the red packages on the right.
Thank you very much for the help!
Your first sentence using "mine" is the correct one.
Mine is a possessive pronoun, so you use it in place of a noun, e.g. "that's mine". My is a possessive adjective (also called a determiner); you use it to describe a noun as your own, e.g. "that's my umbrella".
*My are the red packages on the right.
This sentence is incorrect, so you definitely shouldn't use it. The word "my" can't stand by itself; it can only occur before another word in a noun phrase (such as "my things").
Mine are the red packages on the right.
This is grammatically correct, but to me it sounds odd. Normally, you use "mine" to describe things you own or have that you can identify from the context. A typical example might be to avoid repeating a previous noun, as in these two sentences:
His hands are warm. Mine are cold.
"Mine" stands for "my hands"; this allows the speaker to avoid repeating the word "hands".
But if you put "mine" at the start of an utterance, it's hard to see how a listener could infer what things of yours you're talking about. That makes your sentence seems strange to me. If you just want to say that you own the packages on the right, I think it sounds more natural to say
The red packages on the right are mine.
Again, I'm not saying the other word order is ungrammatical, just that it doesn't sound as good to me.