How many fixtres with 2 60watt, incandescent bulbs can be installed on a circuit wired with #14 awg

Mathematically a 15 amp circuit (that is what #14 cable is rated at) will support 1800 Watts. (120V X 15A = 1800 Watts).

However since this is a multi outlet circuit, you are restricted to 80% of the load (1800 X .8 = 1440 Watts)

That would mean that you would be limited to 1440 / 60 = 24 lamp sockets.