When seen through a mirror, an analog clock shows quarter to four. The correct time shows by the clock:

When viewing an analog clock in a mirror, the image is horizontally flipped. The mirror image shows quarter to four, which is 3:45.

For analog clocks, the mirror reflection follows the principle:

Actual time = 12:00 - Mirror time

This is because the clock face is symmetric about the vertical axis passing through 12 and 6.

Given mirror time = 3:45

Actual time = 12:00 - 3:45

Converting to calculate:

$12:00 - 3:45 = 11:60 - 3:45$

$= 8:15$

At 8:15 on the actual clock:

• Hour hand: slightly past 8
• Minute hand: at 3 (pointing to 15 minutes)

When reflected in a mirror:

• Hour hand appears slightly before 4 (from the mirrored perspective)
• Minute hand appears at 9 (pointing to 45 minutes)

This gives the mirror image of 3:45 (quarter to four).

Therefore, the correct time shown by the clock is 8:15.