Methylates the 2'-O-ribose of nucleotides at positions 32 and 34 of the tRNA anticodon loop of tRNA(Phe), tRNA(Trp) and tRNA(Leu(UAA)). Requires TRM732 for methylation of the cytidine at position 32 and RTT10/TRM734 for methylation of the nucleotides at position 34 in substrate tRNAs. Lack of either of these modifications in tRNA(Phe) reduces formation of wybutosine from 1-methylguanosine at position 37. cytidine(32)/guanosine(34) in tRNA + 2 S-adenosyl-L-methionine = 2'-O-methylcytidine(32)/2'-O-methylguanosine(34) in tRNA + 2 H(+) + 2 S-adenosyl-L-homocysteine Interacts with TRM732; for 2'-O-methylation of cytidine 32 in substrate tRNAs. Interacts with RTT10/TRM734; for 2'-O-methylation of position 34 in substrate tRNAs. Causes severe growth and translation defects, which is due to reduced decoding of Phe codons by hypomodified tRNA(Phe). Present with 4110 molecules/cell in log phase SD medium. Belongs to the class I-like SAM-binding methyltransferase superfamily. RNA methyltransferase RlmE family. TRM7 subfamily.