The two prongs of a power cord are meant to carry current to and from a lamp. If you were to plug only one of the prongs into an outlet, the lamp wouldn't light at all. Why wouldn't it at least glow at half its normal brightness

No it wont glow at all not even a bit!

Explanation:

Electricity is the flow current and current can only flow if the path is complete like a circle where you start from a point and return to the same point.

We need to plug both prongs of the power cord into the outlet so that current can flow from one prong to the second thus completing the circuit.

Why wouldn't it at least glow at half of its brightness ?

It won't glow even a little bit because there is no flow of current. Current only flows when it sees least resistant in its path and in this case current sees infinite resistance since the path is broken so we have to plug the both prongs to let the current flow.

the correct answer is d