Finding a polynomial with given roots, degree, and specific coefficient 
Find a degree 4 polynomial having zeros -6, -3, 2 and 6 and the coefficient of $x^4$ equal 1

The first step is something like $p(x)=c(x-6)(x+3)(x-2)(x-6)$ as those are all the 4 zeros. 
The coefficient of $x^4$ equal to 1 is throwing me off though. 

You are almost right and almost done. That first factor should be $x+6$, not $x-6$ (which you have twice). Any value of $c\neq 0$ will give you a polynomial with the roots in the right place.
And when you multiply out what you have,
$$c(x+6)(x+3)(x-2)(x-6) = cx^4 + (\text{lower terms}).$$
So if you want the coefficient of $x^4$ to be $1$, then $c$ should be...
