Solution:

The height \( h \) at which gravity decreases by 36% (to 64% of its surface value) is found using:

\[
g_h = \frac{gR^2}{(R + h)^2}.
\]

Setting \( g_h = 0.64g \):

\[
0.64 = \frac{R^2}{(R + h)^2}.
\]

Taking the square root:

\[
0.8 = \frac{R}{R + h}.
\]

Cross-multiplying gives:

\[
0.8(R + h) = R \implies 0.8h = 0.2R \implies h = 0.25R=R/4
\]

Thus, the height is R/4.