1. The problem states that $3A = 2B = 6C$. We need to find the ratio $A : B : C$. 2. Let the common value be $k$, so: $$3A = 2B = 6C = k$$ 3. From this, express each variable in terms of $k$: $$A = \frac{k}{3}, \quad B = \frac{k}{2}, \quad C = \frac{k}{6}$$ 4. To find the ratio $A : B : C$, write: $$A : B : C = \frac{k}{3} : \frac{k}{2} : \frac{k}{6}$$ 5. Remove $k$ since it is common: $$= \frac{1}{3} : \frac{1}{2} : \frac{1}{6}$$ 6. Find a common denominator to express all terms as integers. The common denominator is 6: $$= \frac{2}{6} : \frac{3}{6} : \frac{1}{6}$$ 7. Simplify the ratio by multiplying all terms by 6: $$= 2 : 3 : 1$$ 8. Therefore, the ratio $A : B : C$ is $2 : 3 : 1$. The correct option is **2 : 3 : 1**.