If HCF of $(p^2-8p+12)$ and $(p^2+4p-12)$ is $(p-a)$, then the value of a is

1. Factor both quadratic expressions by splitting the middle term:
$$\text{First Expression: }{p}^2-8p+12=p^2-6p-2p+12=p(p-6)-2(p-6)=(p-2)(p-6)$$
$$\text{Second Expression: }{p}^2+4p-12=p^2+6p-2p-12=p(p+6)-2(p+6)=(p-2)(p+6)$$
The Highest Common Factor (HCF) is the factor common to both expressions:
$$\text{HCF}=(p-2)$$
Compare this to the given HCF $(p-a)$:
$$p-a=p-2⟹a=2$$