how we promote my gig at Facebook can I share in big facebook group?
That’s called spamming.
You can share your gig with your target audience and only if they are interested in your services, otherwise commenting in big groups will be considered as spam.
You can share as long as you don’t spam the facebook group, there may be potential buyers on that group but make sure you notify the group admin before posting. You can also share with your friends and family on your personal page.