Hello, could somebody steer me in the right direction into doing this.

The graph with equation y=x^2+2x-8 is reflected in the y-axis then reflected in the x-axis.
I don't get this part because it involved two reflections. I am only used to doing one.

Thanks

Just do them in order. When you reflect in the y-axis the positive x values become negative and the negative x values become positive, like this:
y = (-x)^2 +2(-x) -8 = x^2 - 2x -8.
Then you reflect in the x axis and so you make the whole thing negative:
y = -(x^2 -2x-8) = -(x^2) +2x+8.