(120 - 62) ÷ 4 × 8

Think of  as  because
multiplication does not necessarily precede division, nor does addition
necessarily precede subtraction.  In those two cases whichever one comes first
going left to right takes precedence.  In other words in your problem, the
division will take precedence over the multiplication because the division
symbol comes before the multiplication symbol.

(120 - 62) ÷ 4 × 8

In , "P" comes first. We see (120 - 62), so
instead of that we will do that first and replace the parentheses with the
number 58 and copy everything else over, like this

(120 - 62) ÷ 4 × 8
        58 ÷ 4 × 8

In , "P" comes first.  But there are no
parentheses, so we go on to the "E".  But there are no exponents, so we go on
to .  So we look for multiplications or divisions,
whichever comes first going left to right.  We come to the division first going
left to right. We see 58 ÷ 4 and so we will do that first and replace the 
58 ÷ 4 with the number  reduced to  and copy everything
else over, like this:

(120 - 62) ÷ 4 × 8
        58 ÷ 4 × 8
            × 8

The only thing left to do is the multiplication.  The 2 cancels into the 8 and
leaves 

(120 - 62) ÷ 4 × 8
        58 ÷ 4 × 8
            × 8

           
           
           

Edwin