Question 100750
The basic expression is: {{{3S+(-1/2)*(6+24(-1/3+(1/4)*S))}}}

Always work inside out:  Start with the innermost parentheses and work out from there.

The innermost parenthesis is:
{{{-1/3+(1/4)*S}}}

We cannot combine the terms, other than to note that {{{(1/4)*S=S/4}}} so we "pop" out to the next level of parenthesis.

We always multiply or divide before we add or subtract (unless there are parenthesis that force us to do otherwise), so the next step is to multiply by 24.
{{{24(-1/3+1/4*S)=-24/3+(24/4)S = -8 + 6S}}}

Now the equation is a bit simpler:
{{{3S+(-1/2)*(6+(-8 + 6S))}}}

The innermost parentheses are easy to remove because they are simply separators.

{{{3S+(-1/2)*(6+-8+6S)=3S+(-1/2)*(-2+6S)}}}

Now we continue by doing the righthand multiplication to handle these parentheses:

{{{(-1/2)*(-2+6S)=(2/2-6/2*S)}}}, which is simply {{{(1-3S)}}}

Substituting back into the expression, we have

{{{3S+1-3S=1}}}, which is the end of the chain of calculations. The elaborate expression that we started with, namely {{{3S+(-1/2)*(6+24(-1/3+(1/4)*S))}}}
is just a complicated way of writing the number 1.