To simplify the expression \( \frac{1}{2} - \frac{3}{x^2} - 4 \), we need to combine the terms. However, since these terms have different denominators, we can't directly combine them without finding a common denominator.

Let's rewrite the expression step by step:

1. Start with the given expression:
\[
\frac{1}{2} - \frac{3}{x^2} - 4
\]

2. Rewrite the constant term \( -4 \) as a fraction with a common denominator. Since the common denominator for all terms would be \( 2x^2 \), we can rewrite \( -4 \) as:
\[
-4 = -\frac{4 \cdot 2x^2}{2x^2} = -\frac{8x^2}{2x^2}
\]

3. Now, rewrite each term with the common denominator \( 2x^2 \):
\[
\frac{1}{2} = \frac{1 \cdot x^2}{2 \cdot x^2} = \frac{x^2}{2x^2}
\]
\[
-\frac{3}{x^2} = -\frac{3 \cdot 2}{2 \cdot x^2} = -\frac{6}{2x^2}
\]
\[
-4 = -\frac{8x^2}{2x^2}
\]

4. Combine all the terms over the common denominator \( 2x^2 \):
\[
\frac{x^2}{2x^2} - \frac{6}{2x^2} - \frac{8x^2}{2x^2} = \frac{x^2 - 6 - 8x^2}{2x^2}
\]

5. Simplify the numerator:
\[
x^2 - 6 - 8x^2 = -7x^2 - 6
\]

6. So the simplified expression is:
\[
\frac{-7x^2 - 6}{2x^2}
\]

Therefore, the simplified form of the expression \( \frac{1}{2} - \frac{3}{x^2} - 4 \) is:
\[
\frac{-7x^2 - 6}{2x^2}
\]