What is the image of point r after a counterclockwise rotation on 270 degrees about the orgin?

I will use ccw for countercloclwise and cw for clockwise for this explination.

A 270 ccw rotation is the EXACT same as a 90 cw rotation.  So to perform a 90 degree cw rotation all that has to be done is swap the x anf y coordinates and change the sign on the y.  As a general form:
(x, y) becomes (y, -x)

In your problem R is at (3, 6) so swap the 3 and 6 to get (6, 3) now change the sign on the 3 to get R' as (6, -3)

I’m having a hard time understanding your question