This is where it all starts to go haywire. In the first term, , the 4 should be –4 (because it's the second element in its row, and the +/– signs should alternate as you go along the row). The next two terms should both be multiplied by –3, so that row of the calculation should read .
Similarly, the whole of the last row of the calculation should have the factor of –5, so it should read
Reading further on, I see that two of those errors get corrected in the next line of the calculation. The parentheses are inserted as they should be, and it's only the sign of the 4 that's still wrong:
So the correct answer should be –16 – 60 + 80 = 4.
Final comment: this is a terrible method for evaluating a determinant. It's far easier and quicker to use elementary row and column operations (even easier to use a calculator with a determinant facility, but maybe that would be cheating).