Count'

-verb
1. to list numbers sequentially
2. to add up; enumerate
3. to include in a reckoning
4. to deserve consideration, to have merit
-noun
5. the act of counting, a calculation
6. the total number resulting from a count
7. Baseball, the number of balls and strikes
8. Law, a distinct charge in an indictment
9. Boxing the call from 1 to 10 by the referee while a boxer is off his face

The lawyer counted (1) 31 separate counters (6) of fraud listed against her client. "This may not count (4) for much." she said, "but I want you to known that I won't give up even if we’re down for the count (8)."

Which of the following instances of the word "count" is matched correctly with the number of its definition?
A. 1
B. 4
C. 6
D. 8

Is it B?

The way you have typed the question(s) seems confusing. The first "counted" is definition 1. The second should be "counts" and is 8, not 6. The third is 4. The fourth, "down for the count" refers to boxing, so is 9.

So, you count how many are correct in the manuscript.

That is how I see it. Except for where it says counters, it should say counts.

Yes, it is B. In the given sentence, the word "count" is being used with the meaning of "to deserve consideration, to have merit," which corresponds to definition number 4. So, in this case, the correct match would be B.