To solve the expression $3(2) + 2(-3) + 4$, we need to follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Here, we have only multiplication and addition/subtraction to consider.

Let's break it down step-by-step:

1. Multiplication: $3 \times 2 = 6$ $2 \times (-3) = -6$

2. Substitute these values back into the expression: $6 + (-6) + 4$

3. Addition/Subtraction: $6 - 6 + 4 = 0 + 4 = 4$

So, the value of the expression $3(2) + 2(-3) + 4$ is $4$.

Would you like further details or have any questions?

Here are five related questions to expand on this topic:

1. How do you solve an expression with multiple parentheses?
2. What is the order of operations and why is it important?
3. How do you handle negative numbers in arithmetic operations?
4. Can you simplify and solve $4(3 - 5) + 6(2 - 8)$?
5. What happens if you change the order of operations in a complex expression?

Tip: Always remember to follow the order of operations (PEMDAS/BODMAS) to ensure you get the correct result in arithmetic expressions.