To simplify this expression, we can first distribute the terms:
(¬A + C) × ¬A × ¬C × (B + ¬C) × ¬B × ¬C
= (¬A × ¬A × ¬C × (B + ¬C) × ¬B × ¬C) + (C × ¬A × ¬C × (B + ¬C) × ¬B × ¬C)

Applying the distributive property:
= (A'AC(B + C)B' + A'C(B + C)B') + (0)
= (0 + A'C(B + C)B')
= (A'C(B + C)B')
= (A'C(B + C)B')

Now, we can simplify the expression C(B + C) as:
C(B + C) = CB + CC = CB + C

Therefore, the final simplified expression is:
A'C(B + C)B' = A'CB' + A'C
= AB' + A'C