For the following reaction, identify the substances being oxidized and reduced (including their oxidation numbers), the oxidizing agent, and reducing agent.

ch4 + 2o2 yields co2 + 2h2o

Not sure about this one but probably. I might be wrong because I often get confused in such questions. But i hope my answer is helpful.
CH4 will be the reducing agent because it is oxidizing it self by oxidizing the carbon and oxidizing the hydrogen while reducing the Oxygen. 
in CH4 Carbon has the valency -4 and H has +1. in CO2 Carbon has the valency of +4 and Hydrogen in H2O has the valency of +2 
in C: -4 to +4 is oxidation
in H: +1 to +2 is also oxidation 
in O: -2 to to -4 is reduction ( in CO2) 
concluding CH4 will be the reducing agent and O2 will be the oxidizing agent. 
Always keep this key in mind: OIL RIG
OIL= Oxidation Is Loosing 
RIG= Reduction is Gaining 
Oxidizing agents always reduce them-self and oxidize other elements 
and Reducing agents being the opposite.