On the moon's surface, the acceleration due to gravity is $1.67\mathit{ m}/s^2$. If the radius of the moon is $1.74\times 10^6\mathit{ m}$, Then the mass of the moon is:

On the moon's surface, the acceleration due to gravity is $1.67\mathit{ m}/s^2$. 

If the radius of the moon is $1.74\times 10^6\mathit{ m}$, 

Then the mass of the moon is $7.6\times 10^{22}\mathit{ kg}$.
Here, the universal gravitation constant $G=6.67\times {10}^{-11}\mathit{ kg}.N/m^2$
Acceleration due to gravity on the moon’s surface, ${\mathrm{g}}_{\mathrm{m}}=1.67 \mathrm{m}/{\mathrm{s}}^2$
The radius of the moon, $R=1.74\times {10}^6\mathit{ m}$
We know that, $\mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2}$

Where, M is the mass of the moon. 
$\Rightarrow \mathrm{M}=\frac{{\mathrm{g}}_{\mathrm{m}}{\mathrm{R}}^2}{\mathrm{G}}$
$\Rightarrow M=\frac{1.67\times 1.74\times 1.74\times {10}^{12}}{6.67\times {10}^{-11}}$
$\Rightarrow M=7.6\times 10^{22}\mathit{ kg}$