Sam Wang decides to evaluate an expression of the form $x +2 \cdot 2+ y$. However, he unfortunately reads each ’plus’ as a ’times’ and reads each ’times’ as a ’plus’. Surprisingly, he still gets the problem correct. Find $x + y$.

[i]Proposed by Edwin Zhao[/i]

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[i]Solution.[/i] $\boxed{4}$
We have $x+2*2+y=x \cdot 2+2 \cdot y$. When simplifying, we have $x+y+4=2x+2y$, and $x+y=4$.
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1. The original expression given is \( x + 2 \cdot 2 + y \).

2. Sam reads each 'plus' as 'times' and each 'times' as 'plus'. Therefore, the expression Sam evaluates is \( x \cdot 2 + 2 + y \).

3. We need to simplify both expressions and set them equal to each other since Sam gets the problem correct.

4. Simplify the original expression:
   \[
   x + 2 \cdot 2 + y = x + 4 + y
   \]

5. Simplify the expression Sam evaluates:
   \[
   x \cdot 2 + 2 + y = 2x + 2 + y
   \]

6. Set the simplified expressions equal to each other:
   \[
   x + 4 + y = 2x + 2 + y
   \]

7. Subtract \( y \) from both sides:
   \[
   x + 4 = 2x + 2
   \]

8. Subtract \( x \) from both sides:
   \[
   4 = x + 2
   \]

9. Subtract 2 from both sides:
   \[
   2 = x
   \]

10. Substitute \( x = 2 \) back into the equation \( x + y = 4 \):
    \[
    2 + y = 4
    \]

11. Solve for \( y \):
    \[
    y = 2
    \]

12. Therefore, \( x + y = 2 + 2 = 4 \).

The final answer is \( \boxed{4} \)