How many degrees will the hour hand move, in the time within which the minute hand moves 240°?

The minute hand completes a full rotation of 360° in 60 minutes.

Speed of minute hand $= \dfrac{360°}{60 \text{ min}} = 6° \text{ per minute}$

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The hour hand completes a full rotation of 360° in 12 hours (720 minutes).

Speed of hour hand $= \dfrac{360°}{720 \text{ min}} = 0.5° \text{ per minute}$

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Time taken for the minute hand to move 240°:

$\text{Time} = \dfrac{240°}{6° \text{ per minute}}$

$\text{Time} = 40 \text{ minutes}$

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In 40 minutes, the hour hand moves:

$\text{Movement} = 0.5° \text{ per minute} \times 40 \text{ minutes}$

$\text{Movement} = 20°$

Therefore, the hour hand moves 20°.