How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)?

The hour and minute hands of a clock coincide 11 times in every 12 hours, approximately every 65.45 minutes (every 12/11 hours). Between 10:00 a.m. and 2:00 p.m. is a 4-hour window. Starting after 10:00 a.m., the coincidences occur at approximately 10:54:33 a.m., 12:00:00 noon, and 1:05:27 p.m. That gives 3 coincidences in this 4-hour interval. The next coincidence would occur around 2:10 p.m., which is outside the window. Hence the answer is 3 times.