Let's solve each of the given expressions step-by-step.

### Expression 1: $-\frac{3}{4} \cdot \frac{12}{-5} \cdot \left( -\frac{25}{6} \right)$

1. Multiply the fractions:
$$-\frac{3}{4} \cdot \frac{12}{-5} = \frac{3 \cdot 12}{4 \cdot 5} = \frac{36}{20} = \frac{9}{5}$$
Note that the negative signs cancel out.

2. Now multiply the result by $-\frac{25}{6}$:
$$\frac{9}{5} \cdot \left( -\frac{25}{6} \right) = -\frac{9 \cdot 25}{5 \cdot 6} = -\frac{225}{30} = -\frac{15}{2}$$

So, the result of Expression 1 is $-\frac{15}{2}$.

### Expression 2: $-2 \cdot \frac{-38}{21} \cdot \frac{-7}{4} \cdot \left( -\frac{3}{8} \right)$

1. Multiply $-2$ by $\frac{-38}{21}$:
$$-2 \cdot \frac{-38}{21} = \frac{76}{21}$$

2. Multiply the result by $\frac{-7}{4}$:
$$\frac{76}{21} \cdot \frac{-7}{4} = \frac{76 \cdot -7}{21 \cdot 4} = \frac{-532}{84} = -\frac{266}{42} = -\frac{133}{21}$$

3. Multiply the result by $-\frac{3}{8}$:
$$-\frac{133}{21} \cdot \left( -\frac{3}{8} \right) = \frac{133 \cdot 3}{21 \cdot 8} = \frac{399}{168} = \frac{133}{56}$$

So, the result of Expression 2 is $\frac{133}{56}$.

### Expression 3: $\frac{11}{12} \div \frac{33}{16} \cdot \frac{3}{5}$

1. Divide $\frac{11}{12}$ by $\frac{33}{16}$:
$$\frac{11}{12} \div \frac{33}{16} = \frac{11}{12} \cdot \frac{16}{33} = \frac{11 \cdot 16}{12 \cdot 33} = \frac{176}{396} = \frac{88}{198} = \frac{44}{99} = \frac{4}{9}$$

2. Multiply the result by $\frac{3}{5}$:
$$\frac{4}{9} \cdot \frac{3}{5} = \frac{4 \cdot 3}{9 \cdot 5} = \frac{12}{45} = \frac{4}{15}$$

So, the result of Expression 3 is $\frac{4}{15}$.

### Expression 4: $\frac{7}{23} \cdot \left[ -\frac{8}{6} - \frac{45}{18} \right]$

1. Simplify inside the brackets:
$$-\frac{8}{6} = -\frac{4}{3}$$
$$\frac{45}{18} = \frac{5}{2}$$

2. Combine the fractions inside the brackets:
$$-\frac{4}{3} - \frac{5}{2} = -\frac{8}{6} - \frac{15}{6} = -\frac{23}{6}$$

3. Multiply the result by $\frac{7}{23}$:
$$\frac{7}{23} \cdot \left( -\frac{23}{6} \right) = -\frac{7 \cdot 23}{23 \cdot 6} = -\frac{7}{6}$$

So, the result of Expression 4 is $-\frac{7}{6}$.

### Summary of Results:
1. $-\frac{15}{2}$
2. $\frac{133}{56}$
3. $\frac{4}{15}$
4. $-\frac{7}{6}$