Find the area between the curves.
\[
x=-2, x=2, y=3 e^{3 x}, y=2 e^{3 x}+1
\]

Step 1 ：We are given two curves, \(y = 3e^{3x}\) and \(y = 2e^{3x} + 1\), and the lines \(x = -2\) and \(x = 2\). We are asked to find the area between these curves.

Step 2 ：The area between two curves is given by the integral of the absolute difference of the two functions over the given interval. In this case, the interval is from \(x = -2\) to \(x = 2\).

Step 3 ：We need to find the integral of \(|3e^{3x} - (2e^{3x} + 1)|\) from -2 to 2.

Step 4 ：The integral is a piecewise function, which means the area between the curves changes depending on the value of \(x\). We need to evaluate this integral to find the numerical value of the area.

Step 5 ：After evaluating the integral, we find that the area between the curves is approximately 133.8 square units.

Step 6 ：Final Answer: The area between the curves is \(\boxed{133.8}\) square units.