Let's solve the expression step by step:

$6 - 2 + 3 \times (2 - 3)^2$

Step 1: Simplify inside the parentheses

$2 - 3 = -1$ So, the expression becomes: $6 - 2 + 3 \times (-1)^2$

Step 2: Square the value inside the parentheses

$(-1)^2 = 1$ Now the expression is: $6 - 2 + 3 \times 1$

Step 3: Multiply

$3 \times 1 = 3$ Now the expression becomes: $6 - 2 + 3$

Step 4: Add and subtract

$6 - 2 = 4$ $4 + 3 = 7$

So, the final answer is: $\boxed{7}$

Do you want any further details or have any questions?

Here are 5 related questions to expand on this:

1. How do you simplify an expression with exponents like $(2 - 3)^2$?
2. What is the order of operations (PEMDAS) and how does it work in solving problems like this?
3. Can you solve an expression with variables, such as $6 - x + 3(x - 3)^2$?
4. How do you handle negative numbers inside parentheses when raised to a power?
5. What happens when you multiply or divide terms with exponents of different signs?

Tip: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to simplify expressions correctly!