The formula to calculate the range of the antenna is given by

$\gamma =\sqrt{2Rh} ...\left(1\right)$

Substitute the values of the known parameters into equation (1) and solve to obtain the required height of the antenna.

$\begin{array}{rcl}4\times {10}^3& =& \sqrt{2\times 6400000\times h}\\ & \Rightarrow & 16\times {10}^6=2\times 64\times {10}^5\times h\\ & \Rightarrow & h=\left(\frac{160}{2\times 64}\right)\mathrm{m}=\left(\frac{10}{8}\right)\mathrm{m}\\ & =& \frac{1000}{8}\times {10}^{-2} \mathrm{m}\\ & =& 125\times {10}^{-2} \mathrm{m}\end{array}$$$$$$$