Would you like to go on a tour around the island in this ox cart?
Literal
This ox-cart [with-で] island one-loop tour do-[won't-you-ませんか].
牛車 (ぎゅうしゃ) is an ox-drawn cart. 島一周めぐり 'tour around the island' stacks 島 'island' + 一周 'one circuit' + めぐり 'tour.' ~しませんか is the polite negative-question invitation form — 'won't you do X?' — softer and more inviting than ~しましょう.