The numeral 6 by itself is an abbreviation for 6/3.
The numeral 6 is also found as the second half of a 7-6 suspension. In this case the full figure is 7/3 – 6/3.
The numeral 6 is also found as the second half of a 9/7 – 8/6 suspension. In this case the full figure is 9/7/3 – 8/6/3.
The numeral 6 is also found in the 6/5 chord. The full figure is 6/5/3. This chord is described in greater detail in the "Figures with the numeral 5" chapter.
The numeral 6 is also found in the 6/4 chord. This is a funny little chord. Unlike the root position chord and the 6 chord, it doesn’t sound right to start or end a phrase with a 6/4 chord. It usually is found in a dependent relationship with other chords (as part of a cadential 6/4- 5/3; or as a passing chord). So it’s pretty rare. If you find one that’s not a cadential 6/4 or a passing chord, double-check to make sure you haven’t made a mistake.
Root-based theorists have trouble with the 6/4 chord. It’s often hard to assign a root to it. That’s the great thing about figured bass. We don’t care. It’s just two intervals about the bass. We don’t try to give it a name past “6/4”.
6/sharp-4 is sometimes found as an interesting resolution of a 7-6 suspension. See the description of the descending tetrachord for an example.
Usually, the full figure is 7/3 – 6 /4-sharp. Sometimes it is 7/5/3 – 6-sharp/4/3.
It is also found in 6/4/2 chords, which is often abbreviated to 4/2 or sharp-4. See “Figures with the numeral 4” for more information.
It is also found in the 6/4/3 chord, which, like its cousin the 6/4 chord, is somewhat rare prior to 1700. By Rameau’s time this chord was common. 6/4/3 chords sound nice and rich.