How would you find out if the enthalpy for the two questions exothermic or endothermic?

Explanation:

The second one is quite simple. CH4 (methane) is the main component for natural gas. It is used to heat houses in many many areas. It it heats a house, it must give off heat. It is exothermic.

The first one is much less common and hard to reason. I think it is easier to see the reverse reaction

O2 ===> 2O

O2 is a fairly stable molecule. It takes energy to break the molecules apart. That makes this reaction endothermic.

So the reaction you are given is just the opposite. It must be exothermic.

2O ===> O2 must be exothermic.