Find X in a Parallelogram: Perimeter 10 with Side Length X-2

The problem involves calculating $X$ for a parallelogram with given side lengths and perimeter. Let's proceed step-by-step:

Step 1: First, recognize that in a parallelogram, opposite sides are equal:
- $AB = CD = 4$ (given)
- $AC = BD = X-2$

Step 2: Use the perimeter formula for the parallelogram:
$P = 2(a + b)$
where $a = AB = 4$ and $b = AC = X-2$.

Step 3: Plug the perimeter value and side lengths into the formula:
$10 = 2(4 + (X - 2))$

Step 4: Simplify and solve for $X$:
$10 = 2(4 + X - 2)$
$10 = 2(X + 2)$

Step 5: Divide both sides by 2 to eliminate the factor:
$5 = X + 2$

Step 6: Subtract 2 from both sides to isolate $X$:
$X = 3$

Therefore, the correct value of $X$ is $3$.

The corresponding choice is option 4.