Question 813918
Let me help just on PART OF question (b).


To move the graph 2 units to the RIGHT, you would do this to x:
(x-2);
that much of the change would be {{{f(x)=(x-2)^3+3(x-2)^2-(x-2)+6}}} and you would need to simplify.  The proper usage or 'grammar' for this might mean changing the name of the function, or may mean to change what is shown in the argument of f; not sure.


The change vertically is simpler.  Move n units up, then increase the ENTIRE expression by n units; move n units down, then decrease the ENTIRE expression by n units.