So to use this codon table for CAU, we must first find C on the left side, A on the top, and U on the right. When this is found, the amino acid will be given to the right of the codon.
From this table, we can see that CAU is a codon for Histidine.
A silent mutation is a mutation that occurs and there is no detectable change in the amino acid sequence. Therefore, the mutation that occurs must still produce the same amino acid - in this case, Histidine must still be produced.
If we look at the table, there is only one other codon that gives the Histidine amino acid. This codon is CAC. So we know that the original codon is CAU and the other codon is CAC - therefore we can say that the third nucleotide in the codon can be mutated from a uracil (U) to a cytosine (C) and still produce histidine, causing a silent mutation.