I didn't read all the replies but, I use BIDMAS, its just the synonyms to yours
Brackets, Indices, Division, Multiplication, Addition, Subtraction.
A and S it doesn't really matter about, whatever order you wish to do them, but I'll point out what you did wrong.
8 - 6 + 4
8 - 10
If you ever get confused, rearrange, as that 8 - 6 + 4 is the same as 8 + 4 - 6. I tell my less mathematically skilled friend to rearrange as often as you can, because its magic rearranging is, within the same side and across both sides of your equation.
What do did was not the solution to 8 - 6 + 4 but was the solution to 8 -(6+4).
Here is a very primary school explanation, I don't mean to sound patronizing, but it is a brilliant was to explain it.
When adding a number, count up (right) that many places on a number line.
So on a number line of:
-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10So from -6, 1 place right is -5, 2 places right is -4.
See the error?