> How can the top statement be equal to the bottom?

It isn't. Consider ¬A ∧ C:

A ∧ (¬B ∨ C) = ⊥ ∧ (¬B ∨ ⊤) = ⊥ ∧ ⊤ = ⊥

C ∨ (¬B ∧ A) = ⊤ ∨ (¬B ∧ ⊥) = ⊤ ∨ ⊥ = ⊤

Also: truth table:

A B C | A∧(¬B∨C) C∨(¬B∧A)

------+------------------

F F F | F F

F F T | F T *

F T F | F F

F T T | F T *

T F F | T T

T F T | T T

T T F | F F

T T T | T T