To separate the charges on the two neutral conducting spheres, the student should bring a positively charged rod near one of the spheres (the left sphere, as stated).
When the positively charged rod is brought near the left sphere, it will induce a separation of charge within that sphere. The electrons in the sphere will be attracted towards the positively charged rod, causing the left side of the left sphere to become negatively charged (due to an accumulation of electrons), while the right side will become positively charged (due to a deficit of electrons). However, in order to fully separate the charges, the student will need to ground the left sphere while the positively charged rod is near it. This allows excess electrons to move from the ground onto the sphere, resulting in the left sphere obtaining a net negative charge after the rod is removed.
The other sphere can remain neutral, but if it is not influenced further, it will still have a neutral charge after the first sphere is charged.
The second option (placing two positively charged rods near each sphere) would not effectively separate the charges, because both spheres would be influenced in the same direction, and they would not develop a net charge of opposite sign.
So, the correct action to take is: She should bring a positively charged rod near the left sphere.