You can apply below classes with "Module Class Suffix", "Gantry 5 Block Varation" or in your "custom HTML".

To hide anything on Large Desktop

.hide-large-desktop

To hide anything on Desktop

.hide-desktop

To hide anything on Mobile

.hide-mobileonly

To show anything only on Mobile

.show-mobileonly

To hide anything on Tablet

.hide-tablet

To hide anything on Large Mobile

.hide-large-mobile

To hide anything on Small Mobile

.hide-small-mobile