To solve the expression \( \frac{1}{2} - \frac{43}{101} + \left( -\frac{1}{3} \right) - \frac{1}{6} \), we need to find a common denominator for all the fractions. The denominators are 2, 101, 3, and 6. The least common multiple (LCM) of these numbers is 606.

Let's rewrite each fraction with the common denominator of 606:

1. \( \frac{1}{2} = \frac{1 \times 303}{2 \times 303} = \frac{303}{606} \)
2. \( \frac{43}{101} = \frac{43 \times 6}{101 \times 6} = \frac{258}{606} \)
3. \( -\frac{1}{3} = \frac{-1 \times 202}{3 \times 202} = \frac{-202}{606} \)
4. \( \frac{1}{6} = \frac{1 \times 101}{6 \times 101} = \frac{101}{606} \)

Now, we can combine these fractions:

\[
\frac{303}{606} - \frac{258}{606} + \frac{-202}{606} - \frac{101}{606}
\]

Combine the numerators over the common denominator:

\[
\frac{303 - 258 - 202 - 101}{606}
\]

Calculate the numerator:

\[
303 - 258 = 45
\]
\[
45 - 202 = -157
\]
\[
-157 - 101 = -258
\]

So, the expression simplifies to:

\[
\frac{-258}{606}
\]

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 6:

\[
\frac{-258 \div 6}{606 \div 6} = \frac{-43}{101}
\]

Thus, the simplified result of the expression \( \frac{1}{2} - \frac{43}{101} + \left( -\frac{1}{3} \right) - \frac{1}{6} \) is:

\[
\boxed{\frac{-43}{101}}
\]