The expression to evaluate and simplify is:

$\frac{3b - 2(1 - b)}{a - 2}$ with the given values $a = 3$ and $b = 2$.

Let's break this down step by step:

Step 1: Substitute $a = 3$ and $b = 2$ into the expression

$\frac{3(2) - 2(1 - 2)}{3 - 2}$

Step 2: Simplify the numerator

$3(2) = 6$ and $1 - 2 = -1$ so $-2(-1) = 2.$

Thus, the numerator becomes: $6 + 2 = 8.$

Step 3: Simplify the denominator

$3 - 2 = 1.$

Step 4: Final simplification

$\frac{8}{1} = 8.$

So, the value of the expression is:

$\boxed{8}.$

Would you like further details or have any questions?

Here are 5 related questions:

1. How would the result change if $b = 1$ instead of 2?
2. Can you solve the same expression for $a = 4$ and $b = 3$?
3. How can you rewrite the expression without parentheses and simplify it symbolically?
4. What happens to the expression when both $a$ and $b$ approach 0?
5. How does the expression change if $a = b$?

Tip: Always simplify the terms inside parentheses first to avoid mistakes in longer calculations.