Step 1: Recall the purpose of cooling a burn.
Cooling takes away the heat still trapped in the skin right after a burn, which limits how deep the injury becomes.
Step 2: Recall why very cold water is avoided.
Ice cold water can squeeze shut the small vessels in the skin around the burn and can drop the body temperature too much if a large area is cooled, both of which can make the wound worse instead of better.
Step 3: Recall the recommended value.
Teaching on burns first aid sets the target at around $15$ degrees Celsius, applied by running water for about fifteen to twenty minutes.
Step 4: Rule out the other values.
$10$, $8$, and $6$ degrees Celsius are all colder than this target range and carry the added risk of vessel narrowing and body cooling.
Step 5: Conclude.
So the ideal cooling temperature for a burnt surface is $15$ degrees Celsius.