A clock with the hour hand pointing West at $3\text{p.m.}$ will have its minute hand at $7:45\text{p.m.}$ pointing towards:

In a standard clock:
* At $3\text{p.m.}$, the hour hand points exactly at the $3$ o'clock position (which normally corresponds to East on a standard compass map).
* The problem states that at $3\text{p.m.}$, the hour hand points West. This implies the clock's orientations are rotated by $180^{\circ }$ relative to a standard compass map:
* $3$ o'clock position = West
* $9$ o'clock position = East
* $12$ o'clock position = South
* $6$ o'clock position = North

At $7:45\text{p.m.}$, the minute hand points exactly at the $45$ -minute mark, which corresponds to the $9$ o'clock position on the dial. According to our modified clock directions, the $9$ o'clock position points directly East.