Question 6939
The rules for evaluating expressions is:
Do all operations in a group, identified by parentheses. Once all groups are evaluated, evaluate the expression.
For all evaluations, do powers and roots first. 
Second, do all multiplication and division.
Third, do all addition and subtraction.
Let's evaluate your expression.
{{{12-(20-2((6^2)/3)2^2)}}}
There is a group {{{(6^2/3)}}} that must be done first. 36/3 = 12.
This gives {{{12-(20-2(12)2^2)}}}
There is a power that must be done next. {{{2^2 = 4}}}.
This gives {{{12-(20-2(12)4)}}}
Now do all multiplication, 2(12)(4)=96.
This gives {{{12-(20-96)}}}
There is a group (20-96) that must be done. This gives
{{{12 - (-76)}}}
Subtracting a negative number is the same as adding a positive one. This gives
{{{12 + 76 = 88}}}. DONE!

Subtraction is really adding the negative of a number. That is, 
a - b is really a + (-b). What we had above was
12 - (-76) is really 12 + (-(-76)). The negative of a negative number is the positive of the number. So it's really 12 + 76.