Given $f(x)$, sketch $p(x) = (1/2)f(2x-6)-3$.
I can't put the graph here. You can just tell me the order of transformation of the graph. What i did by myself is horizontal compressing (using $2x$ in the equation) then shift the graph 6 units down (using $-6$ in the graph). Then, I did the vertical stretching (using 1/2). Finally, I move the graph down 3 units (using $-3$). Did i do it right? If not, can you give me the correct order.
You're almost right. Mostly, in this case it's important to first look at the transformation within the function argument (so in this case $2x-6$) and then at the outer modifications.
So you'd compress the graph horizontally by factor 2 (seen from the origin) and then move it 6 units to the right (not to the left!) and then compress it by factor 2 vertically (with respect to the x-axis) and finally move it 3 units downwards.