Let's break down and simplify each of the given mathematical expressions step by step.

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

1. Simplify the first multiplication:
\[ -\frac{3}{4} \cdot \frac{12}{-5} = \frac{3 \cdot 12}{4 \cdot 5} = \frac{36}{20} = \frac{9}{5} \]

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

So, the simplified result for Expression 1 is:
\[ -\frac{15}{2} \]

### Expression 2:
\[ -20 \cdot -\frac{38}{21} \cdot -\frac{7}{4} \cdot \left( -\frac{3}{8} \right) \]

1. Simplify the first multiplication:
\[ -20 \cdot -\frac{38}{21} = \frac{20 \cdot 38}{21} = \frac{760}{21} \]

2. Multiply the result by the third fraction:
\[ \frac{760}{21} \cdot -\frac{7}{4} = \frac{760 \cdot -7}{21 \cdot 4} = \frac{-5320}{84} = -\frac{5320}{84} \]

3. Simplify the fraction:
\[ -\frac{5320}{84} = -\frac{1330}{21} \]

4. Now multiply by the fourth fraction:
\[ -\frac{1330}{21} \cdot -\frac{3}{8} = \frac{1330 \cdot 3}{21 \cdot 8} = \frac{3990}{168} = \frac{665}{28} \]

So, the simplified result for Expression 2 is:
\[ \frac{665}{28} \]

### Expression 3:
\[ \frac{11}{12} : \frac{33}{16} \cdot \frac{3}{5} \]

1. Division of fractions is equivalent to multiplying by the reciprocal:
\[ \frac{11}{12} \div \frac{33}{16} = \frac{11}{12} \cdot \frac{16}{33} = \frac{11 \cdot 16}{12 \cdot 33} = \frac{176}{396} \]

2. Simplify the fraction:
\[ \frac{176}{396} = \frac{44}{99} = \frac{4}{9} \]

3. Now multiply by the third fraction:
\[ \frac{4}{9} \cdot \frac{3}{5} = \frac{4 \cdot 3}{9 \cdot 5} = \frac{12}{45} = \frac{4}{15} \]

So, the simplified result for Expression 3 is:
\[ \frac{4}{15} \]

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

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

2. Perform the subtraction inside the brackets:
\[ -\frac{4}{3} - \frac{5}{2} \]

3. Find a common denominator (6):
\[ -\frac{4}{3} = -\frac{8}{6} \]
\[ \frac{5}{2} = \frac{15}{6} \]

4. Subtract the fractions:
\[ -\frac{8}{6} - \frac{15}{6} = -\frac{23}{6} \]

5. Now multiply by the first fraction:
\[ \frac{7}{23} \cdot -\frac{23}{6} = \frac{7 \cdot -23}{23 \cdot 6} = -\frac{7}{6} \]

So, the simplified result for Expression 4 is:
\[ -\frac{7}{6} \]

### Summary of Simplified Results:
1. \[ -\frac{15}{2} \]
2. \[ \frac{665}{28} \]
3. \[ \frac{4}{15} \]
4. \[ -\frac{7}{6} \]