Step 1: Idea:
The equation says that $2x$ and $3y$ together make 18. Since $y = 2$, we can first work out what $3y$ contributes.
Step 2: Find the part from y:
$3y = 3 \times 2 = 6$. So the rest of the 18 must come from $2x$.
Step 3: Find x:
$2x = 18 - 6 = 12$, so $x = 12 \div 2 = 6$.
Step 4: Verify by putting the values back:
$2(6) + 3(2) = 12 + 6 = 18$. The equation holds, so option 1 is right and the others fail this check.
Final Answer:
So $x = 6$.
\[ \boxed{x = 6} \]