Answer
The tension in the cable would be $1.98\times 10^{20}~N$.
Work Step by Step
The tension in the cable would be equal to the gravitational force between the earth and the moon. Therefore;
$T = \frac{G~M_e~M_m}{r^2}$
$T = \frac{(6.67\times 10^{-11}~m^3/kg~s^2)(5.97\times 10^{24}~kg)(7.35\times 10^{22}~kg)}{(3.84\times 10^{8}~m)^2}$
$T = 1.98\times 10^{20}~N$
The tension in the cable would therefore be $1.98\times 10^{20}~N$.
