Take another look at the sentence:

If Della hadn't __________ the leaky take-out container of moo goo gai pan on the top shelf of the refrigerator, she would not have had to mop up the ooze that dripped over four shelves of food.

Della put the take-out container on the top shelf. Thus, you need a form of lay. Since the sentence has the auxiliary verb had, you need the past participle. Consult the table below or review the rules.

Infinitive Definition Simple Present Simple Past Past Participle Present Participle
to lay to put something down lay(s) laid laid laying
to lie to rest or recline lie(s) lay lain lying

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