I got CS6 Design & Web Premium on my mac, but now i also want it on my new macbook is it possible to use it also on my macbook? thanks!

yes, all adobe single user licenses allow up to two concurrent installations and activations.  if you need the installation file:

Downloadable installation files available:

• Suites and Programs:  CC 2014 | CC | CS6 | CS5.5 | CS5 | CS4, CS4 Web Standard | CS3
• Acrobat:  XI, X | 9,8 | 9 standard
• Premiere Elements:  13 | 12 | 11, 10 | 9, 8, 7 win | 8 mac | 7 mac
• Photoshop Elements:  13 |12 | 11, 10 | 9,8,7 win | 8 mac | 7 mac
• Lightroom:  5.7.1| 5 | 4 | 3
• Captivate:  8 | 7 | 6 | 5.5, 5
• Contribute:  CS5 | CS4, CS3
• FrameMaker:  12, 11, 10, 9, 8, 7.2

Download and installation help for Adobe links

Download and installation help for Prodesigntools links are listed on most linked pages.  They are critical; especially steps 1, 2 and 3.  If you click a link that does not have those steps listed, open a second window using the Lightroom 3 link to see those 'Important Instructions'.