Take a look at the sentence again:
Bathing Noodle, our poodle, requires four arms to hold him in the tub, towels
to mop up the water, and __________.
The blank requires a noun followed by an infinitive phrase. You chose raincoats as protection against the oncoming deluge. You have a noun, raincoats, but as protection against the oncoming deluge is a string of prepositional phrases. Before you continue, review the rules for parallel structure.
Go back to the sentence to try again.