Four sets of earrings is 2*4=<<2*4=8>>8 earrings.
Since for one earring, she uses two magnets, for eight earrings she uses 2*8=<<2*8=16>>16 magnets.
Since she uses half as many buttons as magnets, then for 8 earrings she would use 16/2=8 buttons.
Since she uses three times as many gemstones as buttons, then in 8 earrings, she will use 8*3=<<24=24>>24 gemstones.
#### 24