The following diagram may help you visualize the situation. Today the tip of the Moon's umbra just grazes the Earth's surface. If the Moon were just slightly farther away from the Earth, the tip would always pass above the Earth's surface. Then, we would see partial but never total solar eclipses. See Homework 1. A10.
P is the orbital period of the planet around the Sun.
The force increases 16-fold. That is the force on the Earth AND the force on the Moon increases 16-fold. The force decreases to one-sixteenth of its original strength. This problem is much like the others we have done yet there were a surprising number of incorrect answers. The basic points were covered in a set of classnotes but are repeated here.