OK, this is one of those that I used to always have to look up. Then I came up with a mnemonic device. 

Pallet is the wood platform goods are stacked on for shipping and storing. (Pallets keep things straight and orderly, just like the two Ls in the spelling.)

Palette is the rounded board artists use to hold and mix paint while they’re working. (Art is fancy, and the spelling of “palette” is too!)

Then, of course, there’s palate, which is the roof of the mouth. That’s an easy one to remember: pal-ATE!

In our line of work, I usually find myself referring to a project’s style and color palette. Use the fancy spelling since you’re describing an assortment of colors, just like a painter would use. — Shelley Flannery