Which of the following is a nonrenewable resource (and why)? A: Natural gas B: Hydrogen fuel cell C: Wind power D: Solar energy

The answer is A: Natural Gas. To understand why, first consider the definition of a non-renewable energy source: 

A non-renewable resource (also called a finite resource) is a resource that does not renew itself at a sufficient rate for sustainable economic extraction in meaningful human time-frames. An example is carbon-based, organically-derived fuel. ("Non-renewable Resource")

In simple terms, it means a resource that, once used, will not be naturally replenished. Unlike the other choices, natural gas, once it has been extracted, is not created again (or at least, not fast enough for it to matter to us). What is natural gas? 

Natural gas is a naturally occurring hydrocarbon gas mixture consisting primarily of methane, but commonly including varying amounts of other higher alkanes, and sometimes a small percentage of carbon dioxide, nitrogen, hydrogen sulfide, or helium. It is formed when layers of decomposing plant and animal matter are exposed to intense heat and pressure under the surface of the Earth over millions of years. ("Natural Gas")

The most important part of that definition, for our purposes, is "over millions of years." This means that even if natural gas was forming, the time it takes, and the need for additional decomposing plant and animal matter, means that for all intents and purposes, what we have on the earth now represents all of the natural gas we can use. Thus, it is not renewable.
Please use the links below to learn more about natural gas and renewable energy sources.