Normally referred to as MTBE (methyl t-butyl ether)......raw materials would be methanol and isobutylene.
If you're only allowed to start with alcohols or alkanes, suggest this route. Start with t-butyl alcohol, dehydration reaction (E1 elimination) to form isobutylene.
React the isobutylene with methanol
Sulphonic acid resin catalyst, heat in distillation column.
(Can't see why anyone would want to start with alkanes!).