"Why did..." "Why'd you throw out that loaf of bread?" "Because it was growing green mold." Theoretically it could stand for "why would" but I can't think of any actually example.

‘Why did’ is by far the most likely but ‘why had’ is possible. A. He’d quit school by then. (He quit school at a time in the past, which affected some later time but still in our past) B. Why’d he done that? (It’s a bit repetitive, since you could just ask ‘Why?’. But it’s not ambiguous since ‘why did’ isn’t possible here.)

The word "why'd" is a contraction of "why did." It combines the word "why" with the auxiliary verb "did." This contraction is commonly used in casual spoken English to ask questions or express curiosity about the reason or cause of a particular action or situation.

Why would

Without the sentence it’s hard to say for sure but my guess is “Why would you or why did you…?” “Why’d you go to the beach without me?”