The vertices are w(2,2), x(4,3), y(5,2), z(4,1) reflect the figure in the y-axis then translate the image 3 units right and 4 down. what are the coordinates?

Lets take the point W(2,2) and  how it transform:-
Reflection in y axis  gives the point  (-2,2)  [the y part stays same and  x becomes negative)..
3 units to the right  changes x coordinate to -2+3 = 1  So  this is point (1,2)
now 4 down changes value of y coordinate   to 2 - 4 = -2

finally we have the result of transformation W' ( 1,-2)

Do the same process with the other 3 points