Second inversion: the six-four chord
Build a six-four chord and understand why it sounds unstable.
The fifth in the bass
Invert the sixth chord once more: move the third up as well. Now the fifth of the triad is at the bottom. This is the second inversion, the six-four chord (marked 6/4): from the bass to the middle note is a fourth, to the top note a sixth.
A triad has no more inversions: three notes, three possible bass notes.
C major: triad, sixth chord, six-four chord
Practice: Which inversion? (1)
Practice: Which inversion? (2)
An unstable chord
A six-four chord sounds unstable even though it is made of tonic notes. The fourth above the bass is to blame: in harmony it asks to resolve.
It most often appears just before the end of a phrase as the cadential six-four: the tonic chord over the dominant in the bass, which moves to the dominant, and then to the tonic.
The cadential six-four: C major over G in the bass → G major → C major
To tell the inversions apart on the staff, look for the fourth. No fourth: root position. A fourth at the top: sixth chord. A fourth at the bottom, above the bass: six-four chord.