To simplify this expression, we need to follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify the expression inside the parentheses first
14 + 6√5 = 14 + 6√5

Step 2: Multiply the value outside the parentheses by the expression we found in step 1
(√5 - 3) * (14 + 6√5)

Step 3: Apply distributive property to multiply (√5 - 3) with 14 and (√5 - 3) with 6√5
= (√5 14 + 6√5) - (3 14 + 3 * 6√5)
= (14√5 + 6√5) - (42 + 18√5)

Step 4: Combine like terms
= 20√5 - 42