$$g = \frac{Gm_e}{r^2}$$
where \(G\) is the gravitational constant, \(m_e\) is the mass of the Earth and \(r\) distance from earth center.
If we want to find the distance from the centre of the Earth where the value of \(g\) is half of its value at the surface, we can set \(g = \frac{g_0}{2}\) and solve for \(r\).
$$\frac{1}{2}g_0 = \frac{Gm_e}{r^2}$$
$$r = \sqrt{\frac{2Gm_e}{g_0}}=\sqrt{2R_e}$$
where \(g_0\) is the acceleration due to gravity at the surface of the Earth and \(R_e\) is the radius of the Earth.
Hence the distance is found to be $$\sqrt{2 R_e}$$ i.e. half way to its centre (about 3200 km below the surface).
