Question

find a third-degree polynomial equation with rational coefficients that has roots -4 and 6+i

Answer 1

third-degree polynomial
has 3 roots meaning x= 3 different values

rational coefficients means the complex roots will come in complex conjugate pairs.

They gave you one real root x= -4, and one complex root x= 6+i
the third root must be the complex conjugate of 6+i

the complex conjugate of a+bi is a- bi (negate the imaginary component)

Answer 2

once you have all three roots:
x= a, x=b and x=c
you write each as
(x-a)=0, (x-b)= 0 and (x-c) = 0
multiply them together to get your polynomial
(x-a)(x-b)(x-c)