Why I cannot see styles in the list of phpBB styles

Auto-Install Applications > PHPBB
It is mostly a version conflict problem between phpBB and Style. If you are using phpBB 3.1.x, make absolutely sure that the style you downloaded is for phpBB 3.1.x. Styles created for phpBB 3.0.x are not compatible!
It is recommended to only download styles from phpBB's Customisation Database as this is a trusted source where all styles have been validated by the Styles Team. 

How to install styles on phpBB