"When do you need boiled crabigator by?" "I need it as soon as possible."
Because the hiragana ends with an う sound, you know this word is a verb. The kanji itself means trust, but the verb vocab version is to ask for or to rely on or to request. When you trust someone you can 頼む them, but only when you trust them. You put it in their hands. You trust them, after all.
But, you're entrusting this task to your friend not because you are busy, but because you want to go have a 楽しい time at the waterpark. Sucker!