There are two statements made, which can be written as two equations:

The sum of two numbers are $21: x+y=21$ The sum of the squares is $261: x^{2}+y^{2}=261$

We are asked to find $x$ and $y$.

Since we have the sums of the numbers and the sums of their squares; we can use the square formula of $x+y$, that

is:

$(x+y)^{2}=x^{2}+2 x y+y^{2} \ldots$ Here, we can insert the known values $x+y$ and $x^{2}+y^{2}$

$(21) 2=261+2 x y \ldots$ Arranging to find $x y:$ $441=261+2 x y$

$441-261=2 x y$

$180=2 x y$

$x y=180 / 2$

$x y=90$

We need to find two numbers which multiply to 90 . Checking the answer choices, we see that in (b), 15 and 6 are given, which sum to $90(15 * 6=90)$ and their squares sum to $261(152+62=225+36=261)$.