To form a rectangle, two distinct horizontal lines and two distinct vertical lines must be chosen from the given set of lines. With 4 horizontal lines, the number of ways to choose 2 is given by the combination formula \(^nC_r = \frac{n!}{r!(n-r)!}\), which is \(^4C_2\). Similarly, for 4 vertical lines, the number of ways to choose 2 is \(^4C_2\). The total number of rectangles is the product of these two combinations: \(^4C_2 \times ^4C_2\). Calculating \(^4C_2 = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6\). Therefore, the total number of rectangles is \(6 \times 6 = 36\). This count includes squares as squares are a specific type of rectangle.