Order of operations to be attended to:

1. Parentheses
2. Exponents
3. Multiplications or divisions
4. Additions or subtractions:

We just do one thing at a time and copy everything else over:

42/3*7-2(5*4+3)

First we look for the highest order of operations that
occurs.  That's parentheses:

We find 5*4+3 in parentheses, so that's where we start: 

Within that parentheses, the highest order of operations that
occurs is multiplication, so we perform the 5*4 and replace
it with 20, copying everything else over:

42/3*7-2(20+3) 

Again we look for what's between parentheses:

We find 20+3 in parentheses, 

Within that parentheses, the highest (ONLY!) order of operations 
that occurs is multiplication, so we perform the 20+3 and 
replace it with 23, and copy everything else over:

42/3*7-2(23)

Now since there is only one number inside that parentheses, 
we can erase the parentheses and just indicate the multiplication,
copying everything else over:

42/3*7-2*23

Now the highest order of operations that appears is multiplication
and division.  Notice that multiplication and division are 
considered to be the same level.

The first multiplication or division that we come to going left to
right is the division 42/3 so we do that and get 14.  We replace the
42/3 by 14, and copy everything else over:

14*7-2*23

Now the first multiplication or division that we come to going left 
to right is the 14*7 so we do that and get 98.  We replace the
14*7 by 98

98-2*23

Now the first multiplication or division that we come to going left 
to right is the 2*23 so we do that and get 46.  We replace the
2*23 by 46.

98-46

Now there's only one subtraction left to do:

52

Edwin