Let's pull it apart...
The quotient of the opposite of 30 and 6
The opposite of 30 is -30 and the quotient of -30 and 6 means -30 divided by 6 or
-30/6 = -5
Now the other part...
Plus the opposite of 8. The opposite of 8 is -8, so plus -8 just means minus 8 or -8. So we have the first part added to the second part...
-5 + (-8) which can also be written -5 - 8
-5 - 8 = -13
