If you sketch the curve f(x) = x²+6x-18=0, it will be concave upwards, which means that if the curve cuts the x-axis, the domain of the function f(x)<0 will be between the two roots of f(x)=0. Thus c and d are not appropriate answers.
Jen already factorized f(x)=(x+6)(x-3).
You will need to find the value of the roots (where the curve cuts the x-axis) and find the appropriate response.
If you need help understanding the interval notation, please post.