Answer: B — $4$

Let the table top have dimensions $10' \times 6'$. Each blue rectangular portion has dimensions $8' \times 2.5'$.

Since each blue rectangle has exactly two sides common with two edges of the table top, each blue rectangle must be placed at a corner of the table. Also, its $8'$ side must lie along the $10'$ side of the table, and its $2.5'$ side must lie along the $6'$ side of the table.

Thus, there are four possible corner positions for a blue rectangle: bottom-left, bottom-right, top-left and top-right.

However, the two blue rectangular portions cannot overlap. Now check the possible pairs of corner placements:

• Bottom-left and bottom-right overlap, so this is not possible.
• Top-left and top-right overlap, so this is not possible.
• Bottom-left and top-left do not overlap, so this is possible.
• Bottom-right and top-right do not overlap, so this is possible.
• Bottom-left and top-right do not overlap, so this is possible.
• Bottom-right and top-left do not overlap, so this is possible.

Hence, the number of possible patterns is:

$4$

Therefore, the correct answer is $4$.