Learn Russian: Он поднимает руку, когда хочет ответить. - He raises his hand when he wants to answer.

The verb поднимает (raises) uses the prefix под-, which indicates upward motion. This is the direct opposite of the с-/со- prefixes you are studying right now, which indicate downward motion or descent. For example, to "lower" or "take down" something would use a с- prefix, like in the verbs спускать or снимать.

Why is it руку instead of рука?

Рука (hand or arm) is the direct object being raised by the subject, so it must take the accusative case. For feminine nouns ending in -а, the accusative ending changes to -у, giving us руку.

Why isn't there a word for "his" before the word "hand" in the Russian sentence?

In Russian, possessive pronouns are usually left out when referring to your own body parts, clothing, or immediate family members as long as the owner is obvious from context. Adding свою (his own) before руку wouldn't be strictly wrong, but it sounds redundant and slightly unnatural to a native speaker.

Why is ответить perfective here?

After the verb хочет (wants), we use the perfective infinitive ответить because he wants to give a single, complete answer. If the sentence was about wanting to engage in the ongoing, continuous process of answering questions in general, you would use the imperfective form отвечать.