Which of the following is a coordinate of the new image of a triangle located at {(-3, 0), (-1, 4), (3, 0)}, after the translation (x + 2, y - 4)?

There is no "the following" to choose among. However, you should be able to calculate the correct coordinates after that translation.

Just add 2 to the x's of each vertex, and subtract 4 from the y's.

The first point transates to
(-1,-4)

You do the others.