How can molecular mass be calculated from vapour density?
According to Wikipedia, the vapour density of a molecule is "the density of a vapour in relation to that of hydrogen". The density of a gas, $\rho$, is proportional to its molecular mass, $M$:

$$\rho = \frac{m}{V} \propto \frac{m}{n} = M$$

where $m$ is the mass of the gas, $V$ is the volume, and $n$ the amount of gas. Therefore, if we denote your compound by $\ce{X}$:

$$\begin{align}
67.5 &amp;= \frac{\rho(\ce{X})}{\rho(\ce{H2})} \\
&amp;= \frac{M(\ce{X})}{M(\ce{H2)}} \\
M(\ce{X}) &amp;= 67.5 \cdot M(\ce{H2}) \\
&amp;= 67.5 \cdot \pu{2 g mol-1} \\
&amp;= \pu{135 g mol-1}
\end{align}$$

Finally, you can use this piece of information to find that the molecular formula is $\ce{C8H9NO}$ as well.