To simplify this expression, let's first expand (4 √ 7 + √23)²:

(4 √ 7 + √23)² = (4 √ 7)² + 2(4 √ 7)(√23) + (√23)²
= 16(7) + 2√(7*23) + 23
= 112 + 2√(161) + 23
= 135 + 2√(161)

Now we subtract 8 √161 from the above result:

(135 + 2√161) - 8√161
= 135 + 2√161 - 8√161
= 135 - 6√161

So, (4 √ 7 + √23)² - 8 √161 simplifies to 135 - 6√161.