Notice that we can convert months to days (using the fact that one month is approximately $30$ days) and then we can convert days to hours (using the fact that one day is $24$ hours). $$\begin{aligned} 4.5\,\text{mo}\amp=\frac{4.5\,\text{mo}}{1}\amp\amp\text{Rewrite as a ratio.}\\ \amp\approx\frac{4.5\,\text{mo}}{1}\cdot\frac{30\,\text{d}}{1\,\text{mo}}\cdot\frac{24\,\text{h}}{1\,\text{d}}\amp\amp\text{Both ratios are needed.}\\ \amp=\frac{4.5\,\cancel{\text{mo}}}{1}\cdot\frac{30\,\cancel{\text{d}}}{1\,\cancel{\text{mo}}}\cdot\frac{24\,\text{h}}{1\,\cancel{\text{d}}}\amp\amp\text{Units may now cancel.}\\ \amp=\frac{4.5}{1}\cdot\frac{30}{1}\cdot\frac{24\,\text{h}}{1}\amp\amp\text{Only h remains.}\\ \amp=4.5\cdot30\cdot24\,\text{h}\amp\amp\text{Multiply.}\\ \amp=3240\,\text{h} \end{aligned}$$ So $4.5$ months is about $3240$ hours.