To solve the expression:

\[ 18 \left( \frac{-3}{2} + \frac{2}{3} \right)^2 - 2 \left( \frac{-1}{2} \right)^2 \left( \frac{-4}{5} \right) + 2 \]

Let's break it down step by step.

1. Simplify the expression inside the first set of parentheses:

\[ \frac{-3}{2} + \frac{2}{3} \]

To add these fractions, we need a common denominator. The common denominator of 2 and 3 is 6.

\[ \frac{-3}{2} = \frac{-3 \cdot 3}{2 \cdot 3} = \frac{-9}{6} \]
\[ \frac{2}{3} = \frac{2 \cdot 2}{3 \cdot 2} = \frac{4}{6} \]

So,

\[ \frac{-9}{6} + \frac{4}{6} = \frac{-9 + 4}{6} = \frac{-5}{6} \]

2. Now, square the result:

\[ \left( \frac{-5}{6} \right)^2 = \frac{25}{36} \]

3. Multiply by 18:

\[ 18 \cdot \frac{25}{36} = \frac{18 \cdot 25}{36} = \frac{450}{36} = \frac{75}{6} = 12.5 \]

4. Simplify the expression inside the second set of parentheses:

\[ \left( \frac{-1}{2} \right)^2 \]

Square the fraction:

\[ \left( \frac{-1}{2} \right)^2 = \frac{1}{4} \]

5. Simplify the third fraction:

\[ \left( \frac{-4}{5} \right) \]

This is already in its simplest form.

6. Multiply these values:

\[ 2 \cdot \frac{1}{4} \cdot \frac{-4}{5} = 2 \cdot \frac{-4}{20} = 2 \cdot \frac{-1}{5} = \frac{-2}{5} \]

7. Add the final 2 to the equation:

\[ 12.5 - \frac{2}{5} + 2 \]

Convert 12.5 and 2 into fractions with a common denominator of 5 to combine them with \(\frac{2}{5}\):

\[ 12.5 = \frac{125}{10} = \frac{125 \cdot 5}{10 \cdot 5} = \frac{625}{50} \]
\[ \frac{625}{50} - \frac{2}{5} + 2 = \frac{625}{50} - \frac{20}{50} + \frac{100}{50} = \frac{625 - 20 + 100}{50} = \frac{705}{50} = 14.1 \]

So, the final answer of \(d\) is:

\[ 14.1 \]