Iwill upvote the right answer

without multiplying, determine the sign of the product (−247,634)(183,758).

the sign of the product is positive because a negative multiplied by a positive is a positive.

the sign of the product is negative because a negative multiplied by a positive is a negative.

the sign of the product is negative because the first number is negative.

the sign of the product is positive because the second number is positive.

I believe the correct answer is The sign of the product is negative because a negative multiplied by a positive is a negative.
However, the third The sign of the product is negative because the first number is negative is not necessarily incorrect.
Even so, I think the second choice (The sign of the product is negative because a negative multiplied by a positive is a negative.) is more likely to be the answer they wanted. 
Hope this helped!! xx