You should be able to if you're level 50. There could be two possible causes according to SE's official forum posting restrictions post - the first is, have you maybe posted 20 posts today? Sadly you're allowed up to a maximum 20 posts per 24 hour period, other than here in New Player Help or the Bug Report/Technical Issues sections. I believe this counter resets at 6PM Japanese time every day.
The other possible cause is do you have multiple characters, and if so, is the character who is level 50 the character currently associated with your forum account? Just having a level 50 character isn't enough, to have the least amount of posting restrictions on the forum your forum account has to be associated with a level 50 or above character (the character details shown under your name currently says your level is level 22 ACN not level 50).
To change which character is associated with your account, click on 'Settings' next to the blue 'Logout' button at the top right of the forum page, then from the menu on the left, select 'Edit Character', and then it will show your currently associated character, and below that, a list of all your characters, with the current one connected to the forum listed with a yellow star. Click on the greyed out star of the character you wish to change to, and then on the little drop down menu in the window of that character, choose a relevant class or Job - ideally one that is level 50 or above (this is very important as it's what the Forum checks to determine your posting restrictions) - you can ignore the other two though as they're just for your profile and are optional. When you're done, click on 'Save Changes' at the bottom right of the page. Your character avatar and details on your posts should now be the character you selected.
One final possibility of why your posting is restricted is your character details might not have updated if you've levelled up in game recently, as the forum gets it's data for your character from your Lodestone page, and that is notorious for being rather slow to update information. Give it a day or so and it should finally update.