I tried and got 32 too

For the first integral:∫-4dy-2dxr= (-4,2)tx=-4ty=2tdx=-4dtdy=2dt∫-8 +8 dt=0For the second integral:∫-4dy-2dxr= (-4,2) + (-8+4, 0-2)tx=-4 -4ty=2 -2tdx=-4dtdy=-2dt∫8dt+8dt=320<=t<=2

or maybe it is a conservative field, and the answer is U(-8,0)-U(0,0) where U= -2x-4y