Hincks is waiting for the circles in the picture to arrange themselves in a very specific way.

The small circles need to be arranged to spell out a word. Circles on the same ring move at the same speed, so they'll always be directly across from each other.

Hincks mentions that "planets" align. Starting with the middle circle, rotate each ring of the "solar system" until the word PLANETS is revealed.

When the circles are arranged to spell out PLANETS, there is another word formed by the remaining circles.

When PLANETS is spelled out on half of the circles, the remaining circles spell the word PATIENT, which is the answer to the puzzle and the way that Hincks would describe himself as he waits for a signal that it's time to do his chores.