Karissa begins to solve the equation:

\[
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4)
\]

Her work is correct and is shown below:

\[
\begin{array}{c}
\frac{1}{2}(x-14)+11=\frac{1}{2} x-(x-4) \\
\frac{1}{2} x-7+11=\frac{1}{2} x-x+4 \\
\frac{1}{2} x+4=-\frac{1}{2} x+4
\end{array}
\]

When she subtracts 4 from both sides, $\frac{1}{2} x=-\frac{1}{2} x$ results. What is the value of $x$?

A. $-1$

B. $-\frac{1}{2}$

C. 0

D. $\frac{1}{2}$

We begin with the equation
$$
\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4).
$$

**Step 1: Expand both sides.**

On the left-hand side, distribute $\frac{1}{2}$ over $(x-14)$:
$$
\frac{1}{2}x - \frac{1}{2}\cdot 14 + 11 = \frac{1}{2}x - 7 + 11.
$$
Combining $-7$ and $11$, we have:
$$
\frac{1}{2}x + 4.
$$

On the right-hand side, distribute the negative sign over $(x-4)$:
$$
\frac{1}{2}x - (x-4) = \frac{1}{2}x - x + 4.
$$
Since $\frac{1}{2}x - x = -\frac{1}{2}x$, the right-hand side becomes:
$$
-\frac{1}{2}x + 4.
$$

Now, the equation is:
$$
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4.
$$

**Step 2: Eliminate the constant.**

Subtract $4$ from both sides to isolate the terms with $x$:
$$
\frac{1}{2}x+4-4 = -\frac{1}{2}x+4-4,
$$
which simplifies to:
$$
\frac{1}{2}x = -\frac{1}{2}x.
$$

**Step 3: Combine like terms to solve for $x$.**

Add $\frac{1}{2}x$ to both sides to collect all $x$ terms on one side:
$$
\frac{1}{2}x + \frac{1}{2}x = 0,
$$
thus,
$$
x = 0.
$$

**Conclusion:**

The value of $x$ that satisfies the original equation is
$$
\boxed{0}.
$$