First, I recommend trying the signal at different points in the garage. If the wireless adapter is USB-based this is trivially easy, but if it’s a PCI adapter (inside the computer) then you might need an external antenna, in which case the ethernet cable might be easier / cheaper after all. Consider the construction of the garage and the placement of the receiving antenna with respect to the wireless router; concrete is a fair absorber of radio waves, and steel rebar can scatter them. If possible, the “line of sight” between the two antennas should be direct- if walls are in the way it should pass through them perpendicularly and not at an angle. An angle of 45 degrees doubles the amount of wall the signal must penetrate. 200 feet is a little far, but it is within theoretical range if there are no obstructions. Yes, a range extender might work, and it might be worthwhile for other reasons too- I don’t see any reason not to try it.