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" ">c:fd(9*l);rt(90);fd(15);lt(90);l=0

Try it online - Supports decimal rotations as well!

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If you would prefer the turtle to be shaped like one, you can add the line t.shape("turtle").

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!

Python 2.7, 151 bytes

h,n=input()
s=1-len(h)
e=enumerate
exec n%6*"h=[''.join(c>' 'and h[y-x-3*s/2>>1][x*2+y*6+s>>2]or c for x,c in e(l))for y,l in e(h)];"
print'\n'.join(h)

Example:

% python2.7 hexarot.py <<<'[["   h e x a   ","  g o n s a  "," n d t r i a ","n g l e s m a", " k e m e s a ","  d l y m a  ","   d d e r   "],-1]'
   a a a a   
  x s i m a  
 e n r s s a 
h o t e e m r
 g d l m y e 
  n g e l d  
   n k d d