Question

Reflect triangle ABC with respect to the x-axis and the y-axis. What are the vertices of triangle A′B′C′?
The vertices of triangle A′B′C′ are A′(−2,−1), B′(−6,−3), and C′.
The vertices of triangle A′B′C′ are A′(−2,1), B′(−1,3), and C′(−6,3).

Answer 1

Reflecting across the x-axis changes (x,y) to (x,−y). Reflecting across the y-axis changes (x,y) to (−x,y). Doing both (in either order) sends (x,y) to (−x,−y).

If the original triangle ABC has vertices A(2,1), B(1,3), C(6,3) (as implied by the second set you wrote), then after both reflections the vertices are
A′ = (−2,−1), B′ = (−1,−3), C′ = (−6,−3).

So the correct A′B′C′ is { (−2,−1), (−1,−3), (−6,−3) }.