The total equivalent conductance G_{T} is given by

I = G_{T}V

G_{T} = I/V = 20A/10V = 2 S

The circuit simplifies as shown in the figure:

1/G_{T} = 1/G_{x} + 1/G_{12}

1/2=1/G_{x} + 1/4

G_{x} = 4 S

Answer is D

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