Is KOC(CH3)3 equivalent to KOH as a base in chemical equations?

This depends completely on the equation in question. For instance, both are strong bases, so if that’s all you’re worried about, yeah, they’re about equivalent. But potassium tert-butoxide is way bulkier than potassium hydroxide, so if sterics are a concern (e.g. in nucleophilic substitution and elimination reactions) then there’s a huge difference. Also, the hydrogen bond in KOH will matter in some reactions, not in others. Those are the big differences that jump out to me, but there may be others.

I think I’m trying to do an E2 rxn, but am completely stuck.

Its a benzene ring combined with another hexene ring and a substiuent of OTs on the hexene ring. With KOC(CH3)3 as the strong base and HO(CH2)CH3 as the bottom. We are supposed to compose the major product.

I though the OTs was removed and a double bond formed to take its place, but apparently not?

I agree that the strong, bulky base favors E2 as the major reaction.

What are OTs?

I got it; I was just adding the double bond to the wrong product. OTs I think is irrelevant, just an abbreviation?

Ah, too bad, this was kind of fun :) I actually have to teach an O Chem review class tomorrow; you inspired me to get my books out and finish preparing.