We rewrite the equation to show as much detail as we can.
CO2 + 4H2O ==> CH4 + 2H2O + heat
So an increase in pressure (5 moles on the left and 3 on the right) will make the shift to the side with the smaller number of moles which is to the right and we want more products; therefore, increased pressure is the way to go. Decreasing T means the reaction will try to produce more heat which means it will shift to the right and that's what we want. Finally, increasing methane and hydrogen (increasing the concn of each) makes the reaction shift to the right (adding more reactants makes the reaction try to get rid of them and it can do that by "reacting" them to form products ;-).)
A caveat here. Decreasing T shift the reaction to the right to form more products and that is desirable; however, remember that decreasing T usually decreases the RATE of reaction; therefore, decreasing T may produce more of the products (AT EQUILIBRIUM) BUT the reaction may be so slow that a snail could move faster. Usually a compromise must be reached between the desirables versus the undesirables. For example, in the N2 + 3H2 ==> 2NH3 (the Haber process for making NH3), the commercial process use VERY high pressures (which increases the RATE and the shift) and lowers the T a little as a compensating factor but not so low that the reaction is too slow and takes a month of Sunday's to produce product. I know this probably is more than you ever wanted to know about Le Chatelier's Principle but this extra information may come in useful some day.