Number of moles of oxygen required for the combustion of hexyne and toluene respectively are

When hexyne $\left({\mathrm{C}}_6{\mathrm{H}}_{10}\right)$ burns, it produce 6 moles of ${\mathrm{CO}}_2$ and 5 moles of ${\mathrm{H}}_2\mathrm{O}$

${\mathrm{C}}_6{\mathrm{H}}_{10}+\left(\frac{17}{2}\right){\mathrm{O}}_2\to 6{\mathrm{CO}}_2+5{\mathrm{H}}_2\mathrm{O}$

$\frac{17}{2}$ moles of $O_2$ is required for the combustion of hexyne

When toluene $\left({\mathrm{C}}_7{\mathrm{H}}_8\right)$ burns, it produce 7 moles of ${\mathrm{CO}}_2$ and 4 moles of ${\mathrm{H}}_2\mathrm{O}$

${\mathrm{C}}_7{\mathrm{H}}_8+9{\mathrm{O}}_2\to 7{\mathrm{Co}}_2+4{\mathrm{H}}_2\mathrm{O}$

9 moles of $O_2$ are required for the combustion of toluene.

Hence the correct answer is (C) $\frac{17}{2}$ and 9.