Evaluate the determinate of the matrix

 -4  5  6

   0  4  4

 -2  -5  4

This explains the procedure........http://www.purplemath.com/modules/determs2.htm

Rewrite  the first two columns again

 -4   5   6   -4   5

  0   4   4    0   4

 -2  -5   4   -2  -5

As explained in the PurpleMath resource, multiply down the diagonals and add the results

[ (-4* 4 * 4 ) + (5 * 4 * -2) + (6 * 0 * -5) ] =  [ -64 + -40 + 0]  = -104

Now, multiply "up" the diagonals  and add the results

[ ( -2 * 4 * 6) + ( -5 * 4 * -4) + ( 4 * 0 * 5)]  = [ -48 + 80 + 0]  = 32

Take the first result and subtract the second  =   -104- 32  = -136

So.......the determinant  = -136

You can verify this using this resource : http://matrix.reshish.com/determinant.php