Learn Dutch: Ik hoor het publiek heel hard juichen. - I hear the audience cheer very loudly.

When you use a verb of perception like horen (to hear), zien (to see), or voelen (to feel) along with another action, that second verb goes to the end of the sentence as a full infinitive. You do not use te before it. This is similar to English, where we say I hear them cheer rather than I hear them to cheer.

The translation says loudly, but the Dutch word is hard. Does hard mean loud in Dutch?

Yes! While hard can mean hard (solid) or fast, when you are talking about sound, it means loud. So heel hard here translates to very loudly.

Could I put juichen right after hoor, like we do in English?

No, Dutch has a strict rule for sentences with two verbs. The first verb (hoor) takes the normal second position in the sentence, but the infinitive (juichen) is pushed all the way to the end. The object (het publiek) and the adverb (heel hard) must go between them.

Is publiek considered singular or plural here?

Even though an audience is made up of many people, het publiek is a singular noun in Dutch. That is why it uses the singular article het.