Solve the math expressions below: 1) $$\left(-\frac{2}{9} + 3\frac{1}{18}\right) \cdot 18$$ 2) $$4\frac{1}{8} \cdot \left(-1\frac{4}{9}\right) - 4\frac{2}{9} \cdot \left(-\frac{3}{8}\right)$$

Let's solve the expressions step by step.

1) $$\left(-\frac{2}{9} + 3\frac{1}{18}\right) \cdot 18$$

First, convert the mixed number to an improper fraction: $$3\frac{1}{18} = \frac{3 \cdot 18 + 1}{18} = \frac{54 + 1}{18} = \frac{55}{18}$$.

Now we have: $$\left(-\frac{2}{9} + \frac{55}{18}\right) \cdot 18$$

To add the fractions, find a common denominator. The least common multiple of 9 and 18 is 18. Convert -2/9 to have a denominator of 18: $$\frac{-2}{9} = \frac{-2 \cdot 2}{9 \cdot 2} = \frac{-4}{18}$$.

Now we have: $$\left(-\frac{4}{18} + \frac{55}{18}\right) \cdot 18$$

Add the fractions: $$\frac{-4 + 55}{18} = \frac{51}{18}$$

Now multiply by 18: $$\frac{51}{18} \cdot 18 = 51$$

So, the result of the first expression is 51.

Answer to 1): 51

2) $$4\frac{1}{8} \cdot \left(-1\frac{4}{9}\right) - 4\frac{2}{9} \cdot \left(-\frac{3}{8}\right)$$

Convert the mixed numbers to improper fractions:

$$4\frac{1}{8} = \frac{4 \cdot 8 + 1}{8} = \frac{32 + 1}{8} = \frac{33}{8}$$

$$1\frac{4}{9} = \frac{1 \cdot 9 + 4}{9} = \frac{9 + 4}{9} = \frac{13}{9}$$

$$4\frac{2}{9} = \frac{4 \cdot 9 + 2}{9} = \frac{36 + 2}{9} = \frac{38}{9}$$

Now we have: $$\frac{33}{8} \cdot \left(-\frac{13}{9}\right) - \frac{38}{9} \cdot \left(-\frac{3}{8}\right)$$

Multiply the fractions:

$$\frac{33}{8} \cdot \left(-\frac{13}{9}\right) = -\frac{33 \cdot 13}{8 \cdot 9} = -\frac{429}{72}$$

$$\frac{38}{9} \cdot \left(-\frac{3}{8}\right) = -\frac{38 \cdot 3}{9 \cdot 8} = -\frac{114}{72}$$

Now the expression is: $$-\frac{429}{72} - \left(-\frac{114}{72}\right)$$

Simplify: $$-\frac{429}{72} + \frac{114}{72} = \frac{-429 + 114}{72} = \frac{-315}{72}$$

Reduce the fraction: $$\frac{-315}{72} = -\frac{35 \cdot 9}{8 \cdot 9} = -\frac{35}{8}$$

Convert to mixed number: $$\frac{-35}{8} = -4\frac{3}{8}$$

So, the result of the second expression is $$-4\frac{3}{8}$$

Answer to 2): $$-4\frac{3}{8}$$