When using lead-sheet symbols for augmented sixth chords, we will treat them as major-minor seventh chords built on ♭$$\hat{6}$$ , since that matches the sonic quality of the augmented sixth chords and is similar to how they occur and are spelled in jazz and popular music. The chords in parentheses are enharmonic respellings of the three augmented sixth chord types.
Therefore, when you are asked to provide lead-sheet symbols for augmented sixth chords, analyze each one as if it is a dominant 7th chord with a misspelled 7th ($$\text{A}^♭$$–$$\text{C}$$–$$\text{E}^♭$$–$$\text{F}^♯$$ instead of $$\text{A}^♭$$–$$\text{C}$$–$$\text{E}^♭$$–$$\text{G}^♭$$).