Answer: $18\frac13$


Finding the amounts of petrol
tank: $44$ litres       $\frac14$ of $44 = 11$
                            $\frac13$ of $44 = 44\div3 = 14\frac23$
                            $\frac23$ of $44=44-14\frac23=29\frac13$

$29\frac13-11=18\frac13$


Finding the quantity as a fraction
The volume of petrol that Andrea put in is the difference between $\frac{2}{3}$ and $\frac{1}{4}$ of a tank.

$\frac23-\frac14=\frac{5}{12}$

$\frac{5}{12}$ of $44$ litres $=\frac{5}{12} \times 44 = \frac{5\times 44}{12}=\frac{5\times11}{3} = \frac{55}{3}=18\frac{1}{3}$