I was asked to make a sweet 16 cake. They lady wants a sheet cake with a purse on top. She doesn't care how I decorate it as long as it has tourquouise, lime green and blue. Anyone have any ideas on how I cna put all these colors together?

Those colours go really well together! I did a MadHatter cake last year with those...see below.

If it's a sheet cake, I'd keep that part white and do a free-standing 3-D purse on top. Make the main purse turquoise, the handle lime green, flowers/dots/stripes/whatever in blue & lime green and maybe the inscription on the cake in turquoise. There's a million variations on what you could do, but there's a suggestion for you.