Learn Russian: Кот не мог пролезть через дыру, пока я ему не помог. - The cat could not squeeze through the hole until I helped him.

The preposition через (through / across) always requires the Accusative case when describing the path or medium of motion. Since дыра (hole) is a feminine noun ending in -а, it changes to дыру in the Accusative.

Why is there a не before помог if the English translation says "until I helped him"?

In Russian, the conjunction "until" is usually expressed with the construction пока не (literally "while not"). The underlying logic is "the cat couldn't squeeze through while I had not helped him." Therefore, the не is strictly required before the verb помог.

How does the verb пролезть get the meaning of "squeeze through"?

It is formed by combining the prefix про-, which often indicates moving through or past a space, with the base verb лезть, which means to climb, crawl, or fit into a tight space. Together, they perfectly describe a cat crawling or squeezing its way through an opening.

Why do we use ему instead of его for "him" at the end of the sentence?

The verb помочь (to help) and its imperfective pair помогать always require their object to be in the Dative case. Even though we just say "helped him" in English, Russian requires the Dative ему (literally "helped to him") rather than the Accusative его.