Step 1: Understand the question.
We have 16 g of methane gas ($CH_4$) at STP. We need the volume it takes up.
Step 2: Recall the molar volume rule.
At STP, one mole of any gas fills 22.4 litres, which is the same as 22400 cubic centimetres.
Step 3: Find the molar mass of methane.
Methane is $CH_4$. Carbon is 12 and each hydrogen is 1.
\[ 12 + (4 \times 1) = 16 \text{ g/mol} \]
Step 4: Find the number of moles.
Moles equals mass divided by molar mass.
\[ n = \frac{16}{16} = 1 \text{ mol} \]
Step 5: Find the volume.
Volume equals moles times molar volume.
\[ V = 1 \times 22400 = 22400 \text{ cm}^3 \]
Step 6: Choose the answer.
The volume is 22400 cm³, which is option 2.
\[ \boxed{22400\ \text{cm}^3} \]