items bought in the shop Toribash site but I can not equip my avatar, how do I equip?

If you are talking of the User Text that you recently purchased then you must go to your deactivated items and click on the little "activate" button.

http://forum.toribash.com/tori_inventory.php

If you are talking about Forum Avatars, then you must go to your "User CP," click on your avatar settings, and upload the desired image.

http://forum.toribash.com/profile.php?do=editavatar

I checked your deactivated and active inventory: you currently has no deactivated items, and in your active inventory theres a chronos emote, which can be confused with a head avatar, if youre not much known with the shop. So thats it, apparently you didnt buy any avatar, you actually bought a emote color, which is the color of the text displayed above your head in-game by using the command '/em'.