Calculate Rectangle Perimeter: Nested Rectangles with Dimensions 6, 4, and 2

To solve this problem, we'll need to determine if all required dimensions for calculating the perimeter of rectangle $ABCD$ are present:

• We'll start by defining the perimeter formula for the rectangle, $P = 2(l + w)$.
• Identify any given lengths in the diagram available for $ABCD$: It's given that $AB = 6$ and presumably $BC = 2$.
• Interpret the given rectangle data in context with the diagram, checking if the other length and width of $ABCD$ can be determined from $AIFE$ and $EFHG$.

After reviewing the data and the diagram details, it becomes apparent that specific side lengths for segments $AD$ or any missing lengths on line $AB$ would not be directly deducible from the description provided.

Therefore, due to insufficient information provided to ascertain the entire length or width of rectangle $ABCD$ and thereby its complete perimeter, we conclude that:

The correct answer to the problem is: Not enough data.