Given a function #g(x)#, to get the graph of #y=g(x-2)# you should shift the graph of #y=g(x)# to the right by 2 units. Then to get the graph of #y=-g(x-2)# you should reflect the graph of #y=g(x-2)# across the #x#-axis. Finally, to get the graph of #y=2-g(x-2)# you should shift the graph of #y=-g(x-2)# up by 2 units.

You can also plot some points to help. Let #f(x)=2-sqrt{x-2}#. Then #f(2)=2-sqrt{0}=2#, #f(3)=2-sqrt{1}=1#, #f(4)=2-sqrt{2} approx 0.59#, #f(5)=2-sqrt{3} approx 0.27#, #f(6)=2-sqrt{4}=0#, #f(7)=2-sqrt{5} approx -0.24#, etc...

graph{2-sqrt(x-2) [-1, 10, -2.5, 2.5]}