Let's simplify the expression step by step:
The expression is: \((18 - 2) + \left( \sqrt{16} \right) / 6 - 2^2\)
1. **Evaluate the parentheses and square root:**
\[
18 - 2 = 16
\]
\[
\sqrt{16} = 4
\]
Now, we rewrite the expression with these values substituted:
\[
(16) + \left( 4 \right) / 6 - 2^2
\]
2. **Evaluate the exponent:**
\[
2^2 = 4
\]
Now, we rewrite the expression again:
\[
(16) + \left( 4 \right) / 6 - 4
\]
3. **Perform the division:**
\[
4 / 6 = \frac{2}{3}
\]
(This can also be left as a decimal, approximately \(0.6667\), but we will keep it as a fraction.)
Now, the expression becomes:
\[
16 + \frac{2}{3} - 4
\]
4. **Combine like terms:**
First, we can simplify \(16 - 4\):
\[
16 - 4 = 12
\]
Now we have:
\[
12 + \frac{2}{3}
\]
5. **Combine \(12\) and \(\frac{2}{3}\):**
To add \(12\) and \(\frac{2}{3}\), we convert \(12\) to a fraction with the same denominator:
\[
12 = \frac{36}{3}
\]
Now, add the two fractions:
\[
\frac{36}{3} + \frac{2}{3} = \frac{36 + 2}{3} = \frac{38}{3}
\]
Thus, the simplified expression is \(\frac{38}{3}\), or as a mixed number, \(12\frac{2}{3}\).