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