Here is an image of the exercise I am doing. I'm supposed to write the figured bass symbol underneath the chord label but I am not sure if this is right. I just put a double sharp next to the 3. Can someone correct me please?
You can write it exactly as you've done it! Double accidentals in figured bass are rare, but they do happen; see Can we use double accidentals in figured bass?
Another option would be to replace the "x3" with just a doublesharp. Since a lone accidental applies to the pitch a third above the bass, just putting a doublesharp by default applies to the F above the bass D♯ (just as the first sample only has a ♭ on the A♭ chord to indicate lowering the third above the bass C).
D#FxA# is the triad of D# in rootposition (neither the 3rd augmentation has to be indicated nor the double sharp of the 5th needs an asignment. This means if there stands a D# as a root note the other intervals (3rd and 5th) will be played as Fx and A#, referring to their function as major 3rd and perfect 5th.
(2. chord: In my opinion C#m implies a G# as a perfect fifth and needs not a sharp in the figured notation, it would need a "natural sign" if it wouldn't be sharpened, like the 3rd would need a # if it was a C#-Major-chord.)
Looking at the next chord EbBG: Eb as a root note of Eb major would imply a Bb, but as we have a B (augmented 5th) we'll have to set here a natural sign.