To solve the equation:

\[
\frac{4}{3\sqrt{10x}} - 4 - 8 = 0
\]

Let's break it down step by step:

1. Combine constants:
\[
\frac{4}{3\sqrt{10x}} - 12 = 0
\]

2. Isolate the fraction:
\[
\frac{4}{3\sqrt{10x}} = 12
\]

3. Solve for \(\sqrt{10x}\):
Multiply both sides by \(3\sqrt{10x}\):
\[
4 = 36\sqrt{10x}
\]

4. Divide both sides by 36:
\[
\sqrt{10x} = \frac{4}{36} = \frac{1}{9}
\]

5. Square both sides to remove the square root:
\[
10x = \left(\frac{1}{9}\right)^2
\]
\[
10x = \frac{1}{81}
\]

6. Solve for \(x\):
\[
x = \frac{1}{810}
\]