HexaGolf: Rotatagons
Python 2, 160 158 156 148 124 bytes
Prepare to be amazed! The resulting text is drawn on a canvas... by a Turtle! :D

from turtle import*
h,n=input()
up()
rt(n*60)
l=0
for c in h:
 write(c);fd(9);l-=1
 if&quot; &quot;&gt;c:fd(9*l);rt(90);fd(15);lt(90);l=0

Try it online - Supports decimal rotations as well!

If you would prefer the turtle to be shaped like one, you can add the line t.shape(&quot;turtle&quot;).
View the revision history to see past versions.
Aliases used:
up() - penup()
rt() - right()
lt() - left()
fd() - forward()
bk() - backward()
Thanks to Sherlock9 for the suggestions!