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Welcome to the Bunnings Workshop community @Kayla1. It's wonderful to have you join us, and many thanks for your question about fixing a laundry tap.
Can you please show us an image of inside the tap handle to determine whether the tap spindle has snapped off entirely or where the grub screw has come loose? From your image, it appears that the spindle shaft has sheered off, and if that's the case, replacing the tap assembly is likely the easiest fix. If the spindle has not snapped, there is likely a hidden grubscrew, which fixes the tap handle onto the assembly. The screw could be hidden under the pin handle, so try unscrewing that.
Please let me know if you have any questions.
Mitchell
