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Here we go:

Start with the first guy in our column...

| row 1: -2 , -9 , 4  row 2: 3 , 7 , -5  row 3: 1 , -6 , 8 | ... circle the -2

= + ( -2 ) ... the + sign is from the sign box

Block out the row and column that the -2 is in:

| row 1: -2 , -9 , 4  row 2: 3 , 7 , -5  row 3: 1 , -6 , 8 | ... circle the -2 and cross out its row and column

= + ( -2 ) | row 1: 7 , -5  row 2: -6 , 8 |
and take the determinant of what is left.

Now, go to the second guy in our column and do the same thing:

| row 1: -2 , -9 , 4  row 2: 3 , 7 , -5  row 3: 1 , -6 , 8 | ... circle the 3 and cross out its row and column = + ( -2 ) | row 1: 7 , -5  row 2: -6 , 8 | - ( 3 ) | row 1: -9 , 4  row 2: -6 , 8 | ...the - sign in front of the ( 3 ) is from the sign box