Read the following quadric equation carefully and answer the questions given below.

Equation 1: ${\mathrm{ a}}^2-7a+d=0$

Equation 2: ${\mathrm{ b}}^2-4b+(d-9)=0$

Note: Roots of the equation 1 are ‘x’ and ‘y’ and the roots of equation 2 are ‘x’ and ‘y – x’ .

Find the value of (d-8)^y

Given two quadratic equations:
Equation 1: $a^2-7a+d=0$
The roots of Equation 1 are given as x and y. Using the relation between roots and coefficients of a quadratic equation:
Sum of roots: $x+y=7$ (Equation A)
Product of roots: $xy=d$ (Equation B)

Equation 2: $b^2-4b+(d-9)=0$
The roots of Equation 2 are given as x and y - x. Using the relation between roots and coefficients:
Sum of roots: $x+(y-x)=4$
Simplifying this, we get:
$y=4$

Now, substitute the value of y in Equation A:
$x+4=7$
$x=3$

Now, substitute the values of x and y into Equation B to find d:
$d=xy=3\times 4=12$

We need to find the value of:
${(d-8)}^y$
Substituting d = 12 and y = 4:
${(12-8)}^4=4^4=256$

Thus, the correct answer is 256.