The Answer is E. But Can You Explain Why?

Obviously you do not understand the second law of thermodynamics.

Maybe you'd prefer a musical version.

I understand the second law of thermodynamics very well. But the question is more subtle than that. You are talking about energy transfer and not work extraction. Can you completely transfer energy from one object to another (the oven can be treated as a thermal source)? Aha.. Now its making sense.. let me think some more

Heat won't pass from a cooler to a hotter,

You can try it if you like but you far better notter!

But heat could pass from coolie to a hottie! But that's nottie!

Because a lens can't make heat hotter.

If a lens could increase energy output, we'd really be in business !!

That's what I was thinking.

I could cook my lasagna at 150°, set a lens on the rack under it, and boost my oven temp to 375°, but only focused on the pan of lasagna.

Maybe it's a "common core" question. We need more clueless idiots. If the lens doesn't work, they are victims, and get welfare.

and the point of this question is what??

A 900 Kelvin temperature object is at a higher state of entropy than a 600 Kelvin temperature object. You cannot transfer energy from a lower-entropy state object to another object and have that second object be at a higher entropy state than the initial lower-entropy state (due only to the transfer). Entropy only goes one way, from higher to lower. [That would be equivalent to stirring a scrambled egg to get an unscrambled egg.]

I think I understand. Thermal radiation will cause the absorbed heat to be remitted after the temperature has reached equilibrium. But what if we have a setup that can reduce emission as such..

The flux can be affected, but not the temperature of the radiation. Eventually the flux leaving the small hole in the sphere will equal the flux entering it. It will be as if the sample and sphere you've drawn are replaced by a mirror.

Does your oven produce only radiant heat? Radiant heat could be focused but some or most of the oven heat will be convective and I cannot see that being focused.

Compare it with solar-thermal power plant,heating by parabolic mirror.