Find the HCF AND LCM of x2+x-6; x2-9 and 6x+18

The expressions are already factored as shown in your work:

$$x^2+x-6 = (x+3)(x-2)$$ $$x^2-9 = (x+3)(x-3)$$ $$6x+18 = 6(x+3)$$

The HCF is the product of the common factors raised to the lowest power they appear in any of the expressions.
The common factor in all three expressions is $(x+3)$.

$$\text{HCF} = (x+3)$$

The LCM is the product of all unique factors (common and non-common) raised to the highest power they appear in any of the expressions.
The unique factors are 6, $(x+3)$, $(x-2)$, and $(x-3)$. Each appears with a maximum power of 1.

$$\text{LCM} = 6(x+3)(x-2)(x-3)$$

The HCF and LCM are:
HCF: $\boxed{(x+3)}$
LCM: $\boxed{6(x+3)(x-2)(x-3)}$