43-{-9+2}2exponent+18dividedinto6{-2}

Is this what you mean?

                 6(-2) 
43 - (-9 + 2)2 + -----
                  18

The rules are remembered by the "word" "PEMDAS" which is to be
thought of as four rules "PE[MD][AS]". The "P" is for "parentheses".
The "E" is for "Exponentials".  The "M" is for "Multiplications". 
The "D" is for "Divisions". The "A" is for "Additions". The "S" is
for "Subtractions"

P---1. Go through left to right looking for the lowest level of parentheses
   with operations to do inside. Do the first one you come to and replace
   the parentheses with what you get.  Keep repeating this step until no
   parentheses are left with operations to do inside.

E---2. Go through left to right looking for exponentials. Do the first one you
   come to and replace the exponential with what you get.  Keep repeating
   this step until no exponentials are left. 

MD--3. Go through left to right looking for both multiplications and divisions.
   Do the first multiplication or division you come to and replace the
   multiplication or division with the result you get.  Keep repeating
   this step until no multiplications or divisions are left. 

AS--4. Go through left to right looking for both additions and subtractions.
   Do the first addition or subtraction you come to and replace the
   additiontion or subtraction with the result you get.  Keep repeating
   this step until no additions or subtractions are left.  You should end up
   with only a number.   

If what you mean is

                 6(-2) 
43 - (-9 + 2)2 + -----
                  18


then go through looking for parentheses first to see if anything can be done
there.

The first parenthetical expression we see is (-9+2), so we combine -9 and 2
to get -7, so we replace (-9+2) by (-7)

              6(-2) 
43 - (-7)2 + -----
               18

There are no more parenthetical expressions with anything to be done inside
them.

Next we go through looking for exponentials.  The only exponential we see is
(-7)2 which gives +49, so we replace (-7)2 by 49

          6(-2) 
43 - 49 + -----
           18 

There are no more parentheses with operations inside, nor any more 
exponentials.

So next we go through looking for multiplications or divisions, and we do the
first one we come to going left to right:

The first one of these we come to is the multiplication 6(-2), which gives -12,
so we replace 6(-2) by -12

           -12 
43 - 49 + -----
            18  

Next we go through again looking for multiplications or divisions, and we do
the first one we come to going left to right:

The first one of these we come to is the division -12/18 which reduces to -2/3,
so we replace the -12/18 by (-2/3)

            
43 - 49 + (-2/3)

Finally we do additions and subtractions left to right as we come to them:

Now we do 43 - 49 and replace that by -6

-6 + (-2/3)

To add two negative numbers we add their absolute values 6 and 2/3, getting
6 2/3 or 20/3, and annex the negative sign, getting -20/3

This is the final answer: -20/3 
 
Edwin
AnlytcPhil@aol.com