The numbers in figured bass represent the interval distance away from the given bass note. To find the notes in the chord, simply use the numbers in your figured bass to count upwards, stacking those notes in the same order as the numbers of your figured bass.

Thus:

6# = Ex (double sharp)

5 = D#

4 = C#

As for what it represents harmonically, that's an interesting question. The figured bass you presented doesn't reflect any of the normally-seen inversions (6/5/3, 6/4/3, 6/4/2). To me, I wonder if we're not getting the full story here - that one of those numbers is perhaps setting up a suspension through anticipation? (The Ex and the D# could be both suspensions for a C# triad, while the C# could in fact be a 4-3 suspension for G#, creating a secondary dominant).

It is difficult to say with any certainty the chord's function without context. Perhaps a picture will help. (I'll edit my answer accordingly).

The numbers in figured bass represent the interval distance away from the given bass note. To find the notes in the chord, simply use the numbers in your figured bass to count upwards, stacking those notes in the same order as the numbers of your figured bass.

Thus:

6# = E#

5 = D#

4 = C#

As for what it represents harmonically, that's an interesting question. The figured bass you presented doesn't reflect any of the normally-seen inversions (6/5/3, 6/4/3, 6/4/2). To me, I wonder if we're not getting the full story here - that one of those numbers is perhaps setting up a suspension through anticipation? (The Ex and the D# could be both suspensions for a C# triad, while the C# could in fact be a 4-3 suspension for G#, creating a secondary dominant).

It is difficult to say with any certainty the chord's function without context. Perhaps a picture will help. (I'll edit my answer accordingly).