Factor the numerator and simplify.
x^2 +x-6=(x+3)(x-2)

so now finding limit of (x-2)(x+3)/(x-2)
you can cancel out the x-2 from both the numerator and denominator, you just need to find the limit of x+3 as x approaches 2, which would just be 5
by
L'Hopital says it's 5.
Factor the numerator as (x+3)(x-2) then cancel out x-2 from the numerator and denominator you'll be left out with x+3 whose limit is 2+3=5 when x tends to 2.