State the multiplicity of (x+2)(x-9)(x-1)(x+2)(x-9)(x-9)(x+4)

(X-9)^3 (x+2)^2 (x-1)^1 (x+4)^1
The multiplicity is the exponent on the factor. Since the factors repeat I write them so you could see easily how to interpret the question.
(X-9) has multiplicity 3
(X+2) has multiplicity 2
(X-1) has multiplicity 1
(X+4) has multiplicity 1
Hope this helps.