We received a couple similar reports at the end of this week and have a fix in QA.
It's hard to say from this screenshot which objective you still need to complete, as your task window (flag button on the left) is closed, and Turael says that throughout the path.
But in the reported cases, they'd equipped a helmet before the objective which tells them to equip a helmet, so needed to remove the helmet and re-equip it, so the action counts.
It might take a few tries due to the panel switching, but in the meantime see if you can quickly tap the helmet icon below your backpack to go to your worn equipment, tap the helmet to remove, then wear it again to (hopefully) complete the equip objective.
Alternatively tap the Home button in the top left, tap Hero, then the Loadout tab, where you should see Worn Equipment and Backpack on one screen.
Incidentally, if you long-press the postage stamps and oddments in your backpack, you should get an option to add them to your currency pouch, which'll free up a couple inventory spaces. :)
Happy Scaping!