Answer
236,000 miles is the maximum distance that the moon can be from Earth and still cause a total eclipse.
Work Step by Step
Let $D_E$ be the sun's distance from Earth and let $D_S$ be the sun's diameter. Let $d_E$ be the moon's distance from Earth and let $d_M$ be the moon's diameter.
Using similar triangles, we can find the maximum distance $d_E$ that the moon can be from Earth and still cause a total eclipse:
$\frac{D_S}{D_E} = \frac{d_M}{d_E}$
$d_E = \frac{d_M~D_E}{D_S}$
$d_E = \frac{(2159~mi)(94,500,000~mi)}{(865,000~mi)}$
$d_E = 236,000~mi$
236,000 miles is the maximum distance that the moon can be from Earth and still cause a total eclipse.
