The equation whose roots exceed by 2 than the roots of $4x^4+32x^3+83x^2+76x+21=0$  is

Given roots are exceeded by 2.

$\Rightarrow \alpha +2=x$

$\Rightarrow \alpha =x-2$

The equation is $4{\left(x-2\right)}^4+32{\left(x-2\right)}^3+83{\left(x-2\right)}^2+76\left(x-2\right)+21=0$

All $x^2$  terms $\Rightarrow 32x^2+64x^2-192x^2+83x^2=-13x^2$

All constant terms $\Rightarrow 46-256+332-152+21=9$

$\therefore$ The equation is $4x^4-13x^2+9=0$