To solve the equation \( 2.3^x = 10 \cdot 3^{12} + 8 \cdot 27^{4} \), we can break it down into manageable steps.

First, let's simplify the right-hand side:

1. Calculate \( 27^{4} \):
\[
27 = 3^3, \quad \text{thus, } 27^{4} = (3^3)^{4} = 3^{12}
\]
Therefore, \( 8 \cdot 27^4 = 8 \cdot 3^{12} \).

2. Substitute back into the equation:
\[
2.3^x = 10 \cdot 3^{12} + 8 \cdot 3^{12} = (10 + 8) \cdot 3^{12} = 18 \cdot 3^{12}
\]

Now the equation simplifies to:
\[
2.3^x = 18 \cdot 3^{12}
\]

Next, we can express \( 3^{12} \) in terms of the base \( 2.3^x \).

3. Rewrite \( 3^{12} \) in terms of base \( 2.3^x \):
\[
2.3^x = 18 \cdot 3^{12}
\]
If we want to find \( x \), we can start by isolating \( 3^{12} \):

Next, we need to express the relationship in simpler terms:
Taking logarithms of both sides can help find \( x \):
\[
\log(2.3^x) = \log(18 \cdot 3^{12})
\]

Using logarithmic properties:
\[
x \log(2.3) = \log(18) + 12 \log(3)
\]

4. Solve for \( x \):
\[
x = \frac{\log(18) + 12 \log(3)}{\log(2.3)}
\]

Now, let's approximate the numerical values:

- Calculate \( \log(18) \), \( \log(3) \), and \( \log(2.3) \):
- \( \log(18) \approx 1.2553 \)
- \( \log(3) \approx 0.4771 \)
- \( \log(2.3) \approx 0.3617 \)

5. Substitute back into the equation:
\[
x \approx \frac{1.2553 + 12 \cdot 0.4771}{0.3617}
\]
\[
x \approx \frac{1.2553 + 5.7252}{0.3617} \approx \frac{6.9805}{0.3617} \approx 19.34
\]

Thus, the approximate solution for \( x \) is:
\[
\boxed{19.34}
\]