Can you hear someone moving around in the next room?

Literal

Next [of-の] room [at-で] someone [subject-が] moving-around is-doing [nominalizer-のが] is-audible [question-か].

動き回る ('to move around, walk about') is a compound verb: 動く + 回る ('circulate'). の serves as nominalizer here, turning the verb phrase into a noun-equivalent, with が marking it as the subject of 聞こえる.