jmc

At 6:48, the minute hand is $\frac{12}{60}(360^{\circ })=72$ degrees from the 12:00 position. The hour hand is $\frac{5\frac{12}{60}}{12}(360^{\circ })=156$ degrees from the 12:00 position. The difference in the two positions is $156^{\circ }-72^{\circ }=\boxed{84}$ degrees.