If $\left(\begin{array}{cc}3& y\\ x& 1\end{array}\right|=\left(\begin{array}{cc}3& 2\\ 4& 1\end{array}\right|$, where x and y are natural numbers, then possible values of x and y are:

The correct options are
A x = 1, y = 8
B x = 2 , y = 4
C x = 4 , y = 2
D x = 8 , y = 1
If
$\left(\begin{array}{cc}3& y\\ x& 1\end{array}\right|=\left(\begin{array}{cc}3& 2\\ 4& 1\end{array}\right|$
$⟹3-xy=3-8$
$⟹xy=8$
$⟹\text{Substituting the values given in the options}$
We get $x=1,y=8;x=2,y=4;x=4,y=2;x=8,y=1$
all satisfies the condition.