Let’s resolve into factors

(x + 1) (x + 3) (x-4) (x-6) + 24

= (x + 1)(x-4)(x + 3)(x-6) + 24

= (x²-4x + x-4)(x²–6x + 3x-18) + 24

= (x²-3x-4)(x²–3x-18) + 24

Let x² – 3x = a

= (a-4)(a-18) + 24

= a²-18a-4a + 72 + 24

= a²-22a + 96

= a²-16a-6a + 96

= a(a-16)-6(a-16)

= (a-6)(a-16)

Putting back the values of a we get,

= (x² – 3x -6)( x² – 3x -16)