What is the measure of the smaller of the two angles formed between the hour hand and
the minute hand of a clock when it is 6:44 p.m.?

A clock is a circle, and a circle always contains 360 degrees. Since there are 60 minutes on a clock, each minute mark is 6 degrees.

$$\frac{360^\circ total}{60 minutes total}=6^\circ per  minute$$

The minute hand on the clock will point at 44 minutes, allowing us to calculate it's position on the circle.

(44 min)(6)=$$264^\circ$$

Since there are 12 hours on the clock, each hour mark is 30 degrees.

$$\frac{360^\circ total}{12 hours total}=30^\circ per  hour$$

We can calculate where the hour hand will be at 6:00.

$$(6 hr)(30)=180^\circ$$

However, the hour hand will actually be between the 6 and 7, since we are looking at 6:44 rather than an absolute hour mark. 44 minutes is equal to $$\frac{44}{60}$$th of an hour. Use the same equation to find the additional position of the hour hand.

$$180^\circ + \frac{44}{60} \times 30 = 202^\circ$$ 

We are looking for the smaller angle between the two hands of the clock. The will be equal to the difference between the two angle measures.

Required answer = $$264^\circ - 202^\circ = 62^\circ$$

So, the answer would be option b)$$ 62^\circ $$.