Half-Life by Valve uses the GoldSrc game engine, which is a highly modified version of what engine?

The answer is incorrect. The GoldSrc game engine, used in Half-Life developed by Valve, is actually a heavily modified version of the Quake Engine, not the Quake Engine itself. The Quake Engine, developed by id Software, provided the foundation for the GoldSrc engine, but Valve made substantial modifications and improvements to create their own unique technology for Half-Life.