If x + y = 12 and xy = 14,

$x+y=12$

On squaring both the sides:

$\Rightarrow(x+y)^{2}=(12)^{2}$

$\Rightarrow x^{2}+y^{2}+2 x y=144$

$\Rightarrow x^{2}+y^{2}=144-2 x y$

Given:

$x y=14$

$\Rightarrow x^{2}+y^{2}=144-2(14)$

$\Rightarrow x^{2}+y^{2}=144-28$

$\Rightarrow x^{2}+y^{2}=116$

Therefore, the value of $x^{2}+y^{2}$ is 116 .