Molar heat of combustion with different fuels
This question is asking which substance has the greatest heat density, or energy released per mass combusted (something like J/g).

$\ce{C2H2}$ has a mass of $26.04\ \mathrm{g/mol}$. Since the $\Delta H$ in its combustion is $1\,630\ \mathrm{kJ/mol}$, you will be looking at a heat density of $\frac{1\,630\ \mathrm{kJ/mol}}{26.04\ \mathrm{g/mol}} = 62.6\ \mathrm{\frac{kJ}{g}}.$

Similarly, for $\ce{C6H14}$, you get $\frac{1\,300\ \mathrm{kJ/mol}}{86.178\ \mathrm{g/mol}} = 15.1\ \mathrm{\frac{kJ}{g}}.$

For $\ce{C2H6}$, you get $\frac{1\,560\ \mathrm{kJ/mol}}{30.07\ \mathrm{g/mol}} = 51.9\ \mathrm{\frac{kJ}{g}}.$

It looks like you were on the right track.