When sodium combines with water to produce sodium hydroxide and hydrogen gas, what is the balanced equation?

All you need to do is to break down the problem one by one, this will help you a lot.

sodium = Na

combines= +

with water = H2O OR H+OH-

to produce = --->

sodium = Na

hydroxide = OH

hydrogen gas = H(g)

Na + H+OH- ---> NaOH + H2(g)

now all you balance out the equation: 

2Na + 2H+OH- ---> 2NaOH + H2(g)