Which of the following situations might lead to a penalty kick being awarded?

A penalty kick is awarded when a foul occurs inside the penalty area by the defending team. In this context, the scenario of a foul by the goalkeeper inside the penalty area is key because goalkeepers have unique responsibilities and restrictions within their own penalty area. If the goalkeeper commits a foul, such as tripping an opponent, handling the ball unfairly, or engaging in reckless behavior, the referee will award a penalty kick to the attacking team as a direct consequence of that misconduct.

The other situations listed do not meet the criteria for a penalty kick: a foul occurring outside the penalty area does not result in a penalty kick; dissent by the coach is typically addressed with a caution or ejection but does not affect the game play directly—not resulting in a penalty; and offside by the attacking team leads to an indirect free kick for the defending team rather than a penalty kick. Thus, the only circumstance here that justifies a penalty kick being awarded is indeed the foul committed by the goalkeeper within the penalty area.