Learn Russian: Не ломай эту игрушку!

In Russian, negative commands (telling someone not to do something) almost always use the imperfective aspect. Even though you are talking about a specific, one-time action right now, the negative word не triggers the imperfective ломай.

How is the imperative form ломай built?

You start with the present tense 'they' form of the verb, which is ломают. Drop the -ют ending to find the stem (лома-). Since the stem ends in a vowel, you add -й to make the informal command.

Why are the words эту игрушку in the accusative case?

The toy is the direct object of the action (the thing being broken). This means the feminine phrase эта игрушка must change to the accusative case, which changes the endings to эту игрушку.

Since this is a negative sentence, could we use the genitive case (этой игрушки) instead?

Yes, Russian sometimes uses the genitive case for direct objects after a negated verb. However, the accusative (эту игрушку) is strongly preferred here because you are pointing out a specific, tangible object right in front of you.