Step 1: Understanding the Concept:
To form a rectangle, we need to select 2 horizontal lines (to form the top and bottom) and 2 vertical lines (to form the left and right sides).
Step 2: Key Formula or Approach:
If there are $m$ horizontal lines and $n$ vertical lines, the number of rectangles is:
\[ ^mC_2 \times ^nC_2 \]
Step 3: Detailed Explanation:
1. Number of horizontal lines ($m$) = 4. Ways to choose 2:
\[ ^4C_2 = \frac{4 \times 3}{2 \times 1} = 6. \]
2. Number of vertical lines ($n$) = 4. Ways to choose 2:
\[ ^4C_2 = \frac{4 \times 3}{2 \times 1} = 6. \]
3. Total rectangles = $6 \times 6 = 36$.
Step 4: Final Answer:
The maximum number of rectangles is 36.