Answer
See the detailed answer below.
Work Step by Step
First, we need to have a third object, like a rod, that is negatively charged. We will call the two spheres A and B. Both spheres are initially neutral, as the author told us.
$\bullet$ We need to approach the rod to sphere A and touch it with this rod. The negative charges, or some of them, are now transferred from the rod to sphere A.
$\bullet$ Move the rod away from A, and now we have a negatively charged sphere.
$\bullet$ Now we need to approach sphere B, which is still neutral, towards sphere A. The side of sphere B that faces sphere A is now polarized since the negative charges repel the electrons in sphere B. The side that faces A is positively charged, and the other side is negatively charged.
$\bullet$ Let the two spheres touch, and the negative charge will spread in both spheres, being evenly distributed.
$\bullet$ Now separate the two spheres.
So we have two spheres with like charges of exactly equal magnitude.
See the graph below.
