From the balanced equation, we can see that 1 mole of CH4 releases 802.3 kJ of heat upon combustion. The mass of 1 mole of CH4 is:
mass CH4 = 16.04 grams
So by ratio and proportion:
mass required = (-268 kJ) / (-802.3 kJ / 16.04 grams)
mass required = 0.334 grams