The expression to evaluate is:

$2x - (3x + 2xy - 3y^2)$

where $x = 6$ and $y = 2$.

Step-by-Step Solution

1. Substitute $x = 6$ and $y = 2$ into the expression: $2(6) - (3(6) + 2(6)(2) - 3(2)^2)$

2. Calculate each term inside the parentheses:

   • $3(6) = 18$
   • $2(6)(2) = 24$
   • $3(2)^2 = 3(4) = 12$

   So, the expression within the parentheses becomes: $18 + 24 - 12$

3. Simplify inside the parentheses: $18 + 24 - 12 = 30$

4. Substitute back to the main expression: $2(6) - 30$

5. Evaluate the remaining terms:

   • $2(6) = 12$

   So, the expression is: $12 - 30 = -18$

Final Answer

The evaluated expression is: $\boxed{-18}$

Would you like more details on any step?

Here are some related questions for practice:

1. What would the result be if $x = 4$ and $y = 3$ for the same expression?
2. How would the result change if the expression were $2x + (3x + 2xy - 3y^2)$?
3. What are the general steps to evaluate expressions with multiple variables?
4. How does distributing the negative sign affect the terms inside the parentheses?
5. How would you factor the expression $3x + 2xy - 3y^2$?

Tip: Always simplify expressions inside parentheses before applying any operations outside.