First lets write it out, then change it to a mixed number, than change it. lets do it:
\(6 \frac{3}{4}\)
Now lets convert it to a mixed number:-
6 × 4 = 24
24 + 3 = 27
\(6 \frac{3}{4}\) as an improper fraction is \(\frac{27}{4}\).
Now we have to inverse this:-
\(\frac{4}{27}\)
So, the reciprocal of \(6 \frac{3}{4}\) is \(\frac{4}{27}\)
Hope I helped ya!! xD