Breaking chocolate bar into small clean rectangles

Since a rectangle is formed by $2$ horizontal segments and $2$ vertical segments, the total number of rectangles (clean and corrupted) can be found by picking $2$ of the $9$ possible horizontal lines and picking $2$ of the $9$ vertical lines, which is ${9 \choose 2} \cdot {9 \choose 2} = 1296$ .

The number of corrupted rectangles can be found by picking $1$ of the $4$ possible horizontal lines above the corrupted piece, $1$ of the $5$ possible horizontal lines below the corrupted piece, $1$ of the $4$ possible vertical lines to the left of the corrupted piece, and $1$ of the $5$ possible horizontal lines to the right of the corrupted piece, which is ${4 \choose 1} \cdot {5 \choose 1} \cdot {4 \choose 1} \cdot {5 \choose 1} = 400$ .

The number of clean rectangles is the difference between the total and the corrupted, which is $1296 - 400 = \boxed{896}$ .