Let’s assume the radius of two circles ${{C}_{1}}$ and ${{C}_{2}}$ be ${{r}_{1}}$ and ${{r}_{2}}$
We all know that, Circumference of a circle (C) $=2\pi r$
And their circumference will be $2\pi {{r}_{1}}$ and $2\pi {{r}_{2}}$.
Then, their ratio is $={{r}_{1}}:{{r}_{2}}$
Given in the question, circumference of two circles is in a ratio of $2:3$
${{r}_{1}}:{{r}_{2}}=2:3$
Now, the ratios of their areas is given as
$=\pi r_{1}^{2}:\pi r_{2}^{2}$
$={{\left( \frac{r1}{r2} \right)}^{2}}$
$={{\left( \frac{2}{3} \right)}^{2}}$
$=\frac{9}{16}$
$=\frac{4}{9}$
Thus, ratio of their areas $=4:9$.