To solve the expression \( \frac{1}{2} - \frac{1}{-3} + \frac{1}{23} + \frac{1}{6} \), we need to handle each term step by step.

First, let's simplify \( -\frac{1}{-3} \):
\[
-\frac{1}{-3} = \frac{1}{3}
\]

Now, the expression becomes:
\[
\frac{1}{2} + \frac{1}{3} + \frac{1}{23} + \frac{1}{6}
\]

Next, we need to find a common denominator to add these fractions. The least common multiple (LCM) of 2, 3, 23, and 6 is 138. We will convert each fraction to have this common denominator.

1. Convert \( \frac{1}{2} \):
\[
\frac{1}{2} = \frac{1 \times 69}{2 \times 69} = \frac{69}{138}
\]

2. Convert \( \frac{1}{3} \):
\[
\frac{1}{3} = \frac{1 \times 46}{3 \times 46} = \frac{46}{138}
\]

3. Convert \( \frac{1}{23} \):
\[
\frac{1}{23} = \frac{1 \times 6}{23 \times 6} = \frac{6}{138}
\]

4. Convert \( \frac{1}{6} \):
\[
\frac{1}{6} = \frac{1 \times 23}{6 \times 23} = \frac{23}{138}
\]

Now, we add these fractions:
\[
\frac{69}{138} + \frac{46}{138} + \frac{6}{138} + \frac{23}{138}
\]

Combine the numerators:
\[
\frac{69 + 46 + 6 + 23}{138} = \frac{144}{138}
\]

Simplify the fraction \( \frac{144}{138} \):
\[
\frac{144}{138} = \frac{72}{69} = \frac{24}{23}
\]

Thus, the simplified result of the expression is:
\[
\frac{24}{23}
\]