She should place a negatively charged rod near the left sphere.

She should place a positively charged rod near the left sphere.
She should place two negatively charged rods near each sphere.
She should place two positively charged rods near each sphere.

It seems like you are describing an experiment or a situation involving charged rods and spheres, but the context or the intended outcome is not clear from your statements. Are these instructions for a specific experiment or a question about what would happen under these conditions? To provide a meaningful response, I would need more information about the scenario.

For example, if you have two uncharged, conductive spheres in close proximity and you want to charge them without touching them, bringing a charged rod near one of the spheres would indeed induce a charge separation.

Here are the effects for each of your statements:

1. She should place a negatively charged rod near the left sphere:
If the spheres are conductive and initially uncharged, bringing a negatively charged rod close to the left sphere would cause electrons to be repelled from the sphere that is nearest to the rod (due to repulsion of like charges). Electrons in the left sphere would move away from the rod, leaving the near side of the sphere positively charged and the far side negatively charged. If the spheres are in contact or connected by a conductor, the charge could redistribute between them.

2. She should place a positively charged rod near the left sphere:
If a positively charged rod is brought near the left sphere, electrons would be attracted to the side of the sphere that is closer to the rod, leaving the far side of the sphere positively charged. As in the previous situation, if the spheres are in contact or connected, the charge would redistribute between them.

3. She should place two negatively charged rods near each sphere:
Bringing two negatively charged rods close to each sphere would repel electrons in each sphere, causing both spheres to have a positive region facing the rods and negative regions away from the rods. This would cause polarization of each sphere.

4. She should place two positively charged rods near each sphere:
Conversely, two positively charged rods would attract electrons in each sphere towards the rods. The sides of the spheres facing the rods would become negatively charged, with positive regions on the sides away from the rods, causing polarization of the spheres.

The outcome would depend on the configuration (whether the spheres are isolated or connected) and what you're trying to achieve (e.g., charge separation, induction, etc). If you can provide more information about the setup or objective, I can give a more precise answer.