Which mode has half steps between 2-3 and 5-6 and begins on the sixth degree of the major scale?

Mixolydian mode

Aeolian mode

The idea is identifying a mode by its interval pattern, specifically where the half steps occur. When you start on the sixth degree of a major scale, you get the Aeolian mode, which is the natural minor. Its pattern of whole and half steps is W H W W H W W. That means the half steps are between the second and third degrees and between the fifth and sixth degrees. So the mode described matches Aeolian exactly. (For reference, other modes have different locations for their half steps, so they wouldn’t fit this pattern.)

Ionian mode

Locrian mode

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