Final answer:
Fire and Mello used RNA interference (RNAi) to discover gene silencing by double-stranded RNA.
Step-by-step explanation:
The method used by Fire and Mello to discover gene silencing by double-stranded RNA is RNA interference (RNAi). RNA interference involves the use of small interfering RNAs or microRNAs that bind to mRNA and prevent translation, leading to gene silencing. Double-stranded RNAs are cleaved by the enzyme DICER and then bound to the RNA-induced silencing complex (RISC) before interacting with mRNA.