Triangle abc below is reflected across the y-axis and then translated 1 unit right and 2 units down.
a) write the coordinates of the vertices of the image after reflection.
b) write a rule for the translation. use arrow notation.
c) write the coordinates of the vertices of the new image after translation.

Any point with coordinates (x, y) reflected across the y-axis is going to have the opposite x value that it did before.
You should be able to find the coordinates yourself for part a. (you didn't provide the original ones so I can't help you there)
Here is the "rule" for a reflection across the y-axis:

And when we go 1 unit to the right and 2 down, that's the same as


Combining those into one rule is pretty simple, Use our result for the first in the second and we would get , so the rule is
.
Part A is asking for the coordinates after the reflection (x, y) ⇒ (-x, y).
Part C is asking for the coordinates after the full translation ⇒ (-x+1, y-2)