To solve the equation

\[
( \frac{2}{6} x + \frac{1}{2} ) \times -\frac{5}{6} = 3,
\]

we start by simplifying it step by step.

**Step 1: Simplify the expression on the left side.**

First, let's isolate the term by dividing both sides by \(-\frac{5}{6}\).

\[
\frac{2}{6} x + \frac{1}{2} = \frac{3}{-\frac{5}{6}}.
\]

The right side simplifies as follows:

\[
\frac{3}{-\frac{5}{6}} = 3 \times -\frac{6}{5} = -\frac{18}{5}.
\]

So we have:

\[
\frac{2}{6} x + \frac{1}{2} = -\frac{18}{5}.
\]

**Step 2: Clear the fractions.**

Next, we'll eliminate the fractions on the left side. We can rewrite \(\frac{2}{6}\) as \(\frac{1}{3}\) and \(\frac{1}{2}\) as \(\frac{5}{10}\) or just leave it as is. We can multiply the entire equation by 30 to clear the fractions:

\[
30 \left( \frac{1}{3} x + \frac{1}{2} \right) = 30 \left( -\frac{18}{5} \right).
\]

This simplifies to:

\[
10x + 15 = -108.
\]

**Step 3: Solve for \(x\).**

Now we isolate \(x\):

\[
10x = -108 - 15,
\]
\[
10x = -123.
\]

Finally, divide by 10:

\[
x = -\frac{123}{10} = -12.3.
\]

Thus, the solution to the equation is:

\[
\boxed{-12.3}.
\]