[Solution] Let $x$ be the number of minutes after 10 o'clock. Let $M, H$ be the positions of the minute hand 6 minutes later and the hour hand 3 minutes earlier, respectively.
If measured in minutes, then $\angle T O M=x+6$,
and $\angle \mathrm{SOH}=20+\frac{x-3}{12}$.
Thus, $x+6=20+\frac{x-3}{12}$, solving for $x$ gives $x=15$.
Therefore, the answer is $(D)$.
36-53 If the current time is between 10:00 and 11:00, and in 6 minutes, the minute hand will be exactly opposite the direction of the hour hand from 3 minutes ago, the exact current time is
(A) 10:05 $\frac{5}{11}$.
(B) 10:07 $\frac{1}{2}$.
(C) 10:10.
(D) 10:15.
(E) 10:17 $\frac{1}{2}$.
(21st American High School Mathematics Examination, 1970)