? Just to throw another spanner in the works:
Doesn't it depend on the height of the "nearby airfield" ? I mean, if the airfield is at sea level then you have indeed got 12,000 ft worth of less dense air to correct for. This appears to be what's being assumed in the calculations.
But suppose the "nearby airfield" is also at 12,000 ft ? Their local QNH is the subscale setting that correctly registers 12,000 ft when you are sitting at the highest point on the airfield. In which case your aircraft is at the same level as the airfield and the answer to the question would also be "12,000 ft "
Wouldn't it ?