30 + 12(29-25)³ - 16 ÷ 4

Do what's in the parentheses first  (29-25) becomes 4, so
replace the (29-25) by (4) and copy everything else over:

30 + 12(4)³ - 16 ÷ 4

There is nothing to do in parentheses, so then we do the
exponent  (4)³ means 4×4×4 or 64 so replace the (4)³ by (64)
and copy everything else over:

30 + 12(64) - 16 ÷ 4

There is nothing to do in parentheses and there are no
exponents, so we look for multiplications and divisions as
we come to them left to right.  The first one is 12(64) which
is 768.  So replace the 12(64) by 768 and copy everything else 
over:

30 + 768 - 16 ÷ 4

There are no parentheses or exponents, and the only multiplication
or division that occurs is the 16÷4 which is 4, so replace the
16÷4 by 4 and copy everything else over:

30 + 768 - 4

There are no parentheses, exponents, multiplications or divisions.
So we do additions and subtractions left to right
The first addition of subtraction we come to is 30+768, which 
equals 798, so we replace 30+768 by 798 and copy the rest over:

798-4

So we do that subtraction and get the final answer as

794

Warning!  The temptation is to do more than one thing at a time 
and save writing, but until you have done enough of these and 
become skilled it is extremely easy to do something in the
wrong order and get the wrong answer.

Edwin