How many times do the hands of a clock coincide between 7 a.m. and 7 p.m.?

The minute hand completes a full circle ($360^\circ$) in 60 minutes, so its speed is $6^\circ$ per minute.
The hour hand completes a full circle ($360^\circ$) in 12 hours (720 minutes), so its speed is $0.5^\circ$ per minute.
The relative speed at which the minute hand gains on the hour hand is $6^\circ - 0.5^\circ = 5.5^\circ$ per minute.

For the hands to coincide, the minute hand must gain $360^\circ$ on the hour hand.
The time taken for the hands to coincide is $\frac{360^\circ}{5.5^\circ/\text{minute}} = \frac{720}{11}$ minutes.
This is approximately 65.45 minutes.

A 12-hour period consists of $12 \times 60 = 720$ minutes.
The number of times the hands coincide in 12 hours is $\frac{720 \text{ minutes}}{\frac{720}{11} \text{ minutes/coincidence}} = 11$ times.

The hands coincide 11 times in any 12-hour period. The only exception to a simple count of 12 coincidences (one per hour) is that the hands coincide exactly at 12:00, which counts as one coincidence for both the "11-12" hour and the "12-1" hour. This means there is no separate coincidence between 11 and 12, and between 12 and 1, other than at 12:00 itself.

The period from 7 a.m. to 7 p.m. is exactly 12 hours. This period includes the 12:00 p.m. coincidence.
The coincidences occur approximately at:

• Between 7 a.m. and 8 a.m. (approx. 7:38 a.m.)
• Between 8 a.m. and 9 a.m. (approx. 8:44 a.m.)
• Between 9 a.m. and 10 a.m. (approx. 9:49 a.m.)
• Between 10 a.m. and 11 a.m. (approx. 10:55 a.m.)
• At 12:00 p.m. (noon)
• Between 1 p.m. and 2 p.m. (approx. 1:05 p.m.)
• Between 2 p.m. and 3 p.m. (approx. 2:11 p.m.)
• Between 3 p.m. and 4 p.m. (approx. 3:16 p.m.)
• Between 4 p.m. and 5 p.m. (approx. 4:22 p.m.)
• Between 5 p.m. and 6 p.m. (approx. 5:27 p.m.)
• Between 6 p.m. and 7 p.m. (approx. 6:33 p.m.)

Counting these, there are 11 coincidences.

The final answer is $\text{B. 11}$.