Are you trying to determine the product of this reaction? It's going to be an E1 elimination. I'll explain how I figured that out:
-Potassium t-butoxide is a strong base and a weak nucleophile, so nucleophilic substitution will be unlikely (and that is a competitive reaction with eliminations). This leaves you with two options: E1 or E2 elimination.
-E2 elimination is unlikely in a polar solvent (t-butanol).
-The substrate molecule has an allylic bromine. If the C-Br bond were to spontaneously break, the carbocation formed would have resonance stabilization. As such, a mechanism involving a carbocation is likely, especially considering that the solvent is polar and can stabilize the carbocation even more.