Why Any oscillator needs two things: gain to make up for circuit losses, and a frequency-selective feedback path that returns part of the output back to the input in phase. That is the Barkhausen condition: loop gain of at least 1 with 0 (or 360) degrees phase shift around the loop. The filter, usually an LC tank, crystal, or RC network, decides which single frequency satisfies that condition, so the amplifier sustains a clean sine wave there.
Watch out A frequency multiplier and mixer are things you add after an oscillator to move or multiply its output, not what generates the oscillation; and note the correct answer says feedback, while the feed-forward choice describes a path that never returns energy to the input.
Oscillator = amplifier + filter + feedback. Gain replaces losses, the filter picks the frequency.