Incorrect Brian.... the multiplication step clears first before adding or subtracting any numbers.

No, you would only multiply the last 1 by zero, as you do multiplication first, by PEMDAS. Then, you would add  or subtract the remainder of the ones.

To answer the question, you would use PEMDAS to answer any math question, especially if there are no parentheses. 

Here is the original:
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1*0

Here, I add my own parentheses, according to PEMDAS:

(1+1+1+1+1+1+1+1+1+1)-1+ (1+ 1+1+1) +1*0

The last phrase = 0, and we evaluate it first, because it's multiplication, so:

(1+1+1+1+1+1+1+1+1+1)-1+ (1+ 1+1+1) + 0

The first phrase =  10, because we're just adding 10 ones together, so:

(10) - 1 + (1+ 1+1+1)

Now, adding the last phrase, since I put it in parentheses:

(10) - 1 + (4)

Now, combine the first two terms:

9 + 4

And then add:

13

Unless there is a typo here, you have a trick question.  Note you have plus and minus signs until the zero.  There appears to be a multiplication sign in front of the zero.  If that's correct, the answer is zero as you just multiplied the entire problem by zero.