In music theory, a minor sixth is an interval that has eight half steps
The minor sixth requires that:
- The interval must be a sixth interval (six note names between the first and the last).
- The interval must have eight half steps.
What does a minor sixth look like?
Here is an example of a melodic minor sixth (two music notes in a melody) and a harmonic minor sixth (in a chord):

How to recognize a minor sixth?
Rule of music theory: All intervals in a major scale starting with the tonic (degree I) are either major or perfect, and only unison, octave, fourth and fifth are perfect (the others are major).
Example with the interval C / A♭ :
Let's take the C major scale to have C as the tonic:

From the rule stated above, the interval C / A♮ is a major sixth, so the interval C / A♭ is a minor sixth.
Inversion of the minor sixth
The inversion of the minor sixth is the major third.
Here is an example of a major third:

Musical examples of minor sixth
Tristan and Isolde, Richard Wagner
The first interval of Richard Wagner's Prélude to Tristan and Isolde is a minor sixth:

The entertainer by Scott Joplin
Scott Joplin's ragtime entitled The entertainer has three consecutive minor sixths:

Interval identification game
You will find this interval in my Intervals identification game: