Start within the innermost set of grouping symbols.

$(6 \div 12) \cdot \lbrack(\require{color}\colorbox{yellow}{$ 84 - 9 $}) \div 5 + 1\rbrack$

$(6 \div 12) \cdot \lbrack \require{color}\colorbox{yellow}{$ 75 $} \div 5 + 1\rbrack$

Simplify within the brackets, using the order of operations.

$(6 \div 12) \cdot \lbrack \require{color}\colorbox{yellow}{$ 75 \div 5 $} + 1\rbrack$

$(6 \div 12) \cdot \lbrack \require{color}\colorbox{yellow}{$ 15 $} \require{color}\colorbox{lime}{$ + 1 $}\rbrack$

$(6 \div 12) \cdot \require{color}\colorbox{lime}{$ 16 $}$

Simplify within the parentheses.

$\left( \require{color}\colorbox{yellow}{$ 6 \div 12 $} \right) \cdot 16$

$\require{color}\colorbox{yellow}{$ \frac{1}{2} $} \cdot 16$

$8$

Simplify within the absolute value symbols and work your way out.

Be sure to follow the order of operations along the way.

$5 \cdot \left( 16 - 2^{4} \right) + 8 \cdot (4 - \left| \require{color}\colorbox{yellow}{$ 12^{2} $} - 11 \cdot 12 \right|)$

$5 \cdot \left( 16 - 2^{4} \right) + 8 \cdot (4 - \left| \require{color}\colorbox{yellow}{$ 144 $} - \require{color}\colorbox{lime}{$ 11 \cdot 12 $} \right|)$

$5 \cdot \left( 16 - 2^{4} \right) + 8 \cdot (4 - \left| \require{color}\colorbox{aqua}{$ 144 - $} \require{color}\colorbox{lime}{$ 132 $} \right|)$

$5 \cdot \left( 16 - 2^{4} \right) + 8 \cdot (4 - \left| \require{color}\colorbox{aqua}{$ 12 $} \right|)$

$5 \cdot \left( 16 - 2^{4} \right) + 8 \cdot (\require{color}\colorbox{violet}{$ 4 - $} \require{color}\colorbox{aqua}{$ 12 $})$

$5 \cdot \left( 16 - 2^{4} \right) + \require{color}\colorbox{yellow}{$ 8 \cdot $} ( \require{color}\colorbox{violet}{$ - 8 $})$

$5 \cdot \left( 16 - \require{color}\colorbox{lime}{$ 2^{4} $} \right) + ( \require{color}\colorbox{yellow}{$ - 64 $})$

$5 \cdot \left( \require{color}\colorbox{aqua}{$ 16 - $} \require{color}\colorbox{lime}{$ 16 $} \right) + \left( - 64 \right)$

$\require{color}\colorbox{pink}{$ 5 $} \cdot \require{color}\colorbox{aqua}{$ 0 $} + \left( - 64 \right)$

$\require{color}\colorbox{pink}{$ 0 $} + \left( - 64 \right)$

$- 64$

Begin working within the first grouping symbol.

Follow the order of operations.

$- 14 + 3 \cdot \left( 18 - \require{color}\colorbox{yellow}{$ 10 \cdot \frac{3}{2} $} \right) - \left| {4.5}^{2} - 25 \right|$

$- 14 + 3 \cdot \left( \require{color}\colorbox{lime}{$ 18 - $} \require{color}\colorbox{yellow}{$ 15 $} \right) - \left| {4.5}^{2} - 25 \right|$

$- 14 + 3 \cdot \require{color}\colorbox{lime}{$ 3 $} - \left| \require{color}\colorbox{aqua}{$ {4.5}^{2} $} - 25 \right|$

$- 14 + 3 \cdot 3 - \left| \require{color}\colorbox{aqua}{$ 20.25 $} \require{color}\colorbox{violet}{$ - 25 $} \right|$

$- 14 + 3 \cdot 3 - \left| \require{color}\colorbox{violet}{$ - 4.75 $} \right|$

$- 14 + \require{color}\colorbox{yellow}{$ 3 \cdot 3 $} - \require{color}\colorbox{violet}{$ 4.75 $}$

$- 14 + \require{color}\colorbox{yellow}{$ 9 $} - 4.75$

$- 9.75$