Question 33824
>>>>>This is correct:
shift f(x)2 units to the right             I got h(x)=f(x-c)=(x-2)^2-8

shift f(x)2 units down                     I got h(x)=x^2+(-8-2)=x^2-6
-in this case, your solution is correct but your final answer is wrong because  -8 - 2 is -10. So, your solution and answer must be like this:
I got h(x)=x^2+(-8-2)=x^2-10

shift f(x)2 units right and 2 units down   I got  h(x)=(x-2)^2+(-8-2)
-in this case, your answer is not the final answer. we may simplify this, so that your answer must be like this:
I got  h(x)=(x-2)^2-10

I change some signs in your questions.

If you have further questions, just contact me. This is my number: 09223011043