You are doing it correctly, you have just made an algebra mistake in step 2. That -28 should be a -4 you accidentally subtracted 12 when you should have added 12.

This is definitely the method you should use by adding scalar multiples of one row to another whenever possible, but you should note that it is also possible to swap rows (you must keep track of these steps because when you interchange two rows it changes the sign of the determinant) and you can multiply a row by a scalar (this multiplies the determinant by that scalar).