A clock reads the time as 6:45. If the minute hand points towards north, in…

Concept: On a clock face, each hour mark corresponds to a fixed compass bearing under the usual orientation (12 = North, 3 = East, 6 = South, 9 = West). When one hand's position is stated to point in a different given direction, the whole dial is understood to be rotated by that same angular offset, so every other mark's compass direction shifts by the identical amount while the spacing between the marks stays unchanged.

1. At 6:45 the minute hand sits exactly at the 9 mark. Under the usual orientation this mark reads West, but here it is given to point North instead - a shift of 90 degrees, since rotating West by 90 degrees lands on North.

2. Apply this same 90-degree shift to every other mark: the 6 mark, which usually reads South, now reads West; the 12 mark now reads East, and so on around the dial.

3. The hour hand at 6:45 has moved 45/60 = 3/4 of the way from the 6 mark toward the 7 mark, since it advances 30 degrees per hour (22.5 degrees past the 6 mark).

4. The 6 mark now reads West and the 9 mark reads North, so the short arc running from the 6 mark to the 9 mark - the arc the hour hand sits inside - spans the North-West quadrant of the compass.

5. The hour hand, positioned three-quarters of the way from the 6 mark toward the 7 mark on that arc, therefore points North-west.

Cross-check: The accompanying diagram marks the 9-position as N and the 6-position as W directly on the dial, with the hour hand's arrow drawn squarely inside the arc between these two labels, confirming the North-west result independently of the angle calculation above.