16-{15-[2(5+2)-4]+6}

Look for the innermost parentheses, (5+2)
Replace the (5+2) by (7).  You cannot remove the ( ) because
they are needed to show the multiplication.  Copy everything 
else over:

16-{15-[2(7)-4]+6}

Look for the innermost parentheses  [2(7)-4] 
Multiplication comes before subtraction, so multiply the 2(7).
Replace the 2(7) by 14.  Copy everything else over:

16-{15-[14-4]+6}

Look for the innermost parentheses:  [14-4]
Replace [14-4] by [10], and then you can drop the [ ] and just
put 10 because there is just one number and it is not multiplied 
by anything.  Copy everything else over:

16-{15-10+6}

Look for the innermost (the only!) parentheses:  {15-10+6}

There is a subtraction and an addition.  Subtractions and additions
are done in the order of left to right. The subtraction comes first
going left to right. Replace 15-10 by 5.  Copy everything else over:

16-{5+6}

Replace the {5+6} by {11}. and the you can drop the { } and just
put 11 because there is just one number and it is not multiplied 
by anything.Copy eveything else over:

16-11

Replace that by

5

Edwin