Answer
See the detailed answer below.
Work Step by Step
First, we need 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 make the two spheres in touch.
$\bullet$ Then we need to approach the rod to sphere A, without touching it with this rod. The negative charges at the top and at the left of the sphere will run away rightward [toward sphere B] and downward.
Now the two spheres are polarized, sphere A is positively charged and sphere B is negatively charged.
$\bullet$ Now we need to separate the two spheres while the rod is still above sphere A. Now the two spheres are equally charged with different charges and hence we can move the rod away.
See the figure below,
