1. Start with the equation \frac{2}{r} = \frac{12}{18} .
2. Simplify the fraction on the right side:
\frac{12}{18} = \frac{2}{3} .
3. Set the simplified equation:
\frac{2}{r} = \frac{2}{3} .
4. Cross-multiply:
2 \cdot 3 = 2 \cdot r .
5. Solve for r :
r = \frac{2 \cdot 3}{2} = 3 .
6. Thus, the value of r is 3.