As the descriptor indicates, the six-four chord arises from neighbouring motion--a double one at that. Ex. 7.3a provides two instances, one applied to I, the other to IV. (Note that the horizontal lines connection 6 to 5 and 4 to 3 in b. 1 is missing.)
Ex. 7.3b - the plagal expansion of the opening tonic using N 6/4 is straightforward enough to understand but note the interesting double passing motion in b. 3: the underlying voices across bs. 2-3 are B-A-G in parallel with G-F#-E.
Ex. 8.16 - the N6/4 progression is internally expanded with an inserted V6/5 by way of a neighbouring motion in the bass.
Now that you have learnt the common uses of the six-four chord, enjoy this ingenious song demonstrating all of them: Six-four chord song.