Both 22 grams of ${CO}_2$ and 8 grams of methane contain the following carbon atoms

 Using the formula: $\mathrm{moles}=\frac{\mathrm{given} \mathrm{mass}}{\mathrm{molecular} \mathrm{mass}}$

Moles of 22g of carbon dioxide would be $\frac{22}{44}=0.5$

Similarly, Moles of 8g of methane would be $\frac{8}{16}=0.5$

We know that 1 mole= $6.022 \times {10}^{23}$

Therefore moles of carbon dioxide and methane = 0.5 + 0.5=1mole = $6.022 \times {10}^{23}$

Hence the correct option is (C).