Step 1: Find the number of moles of phenol.
The molecular weight of phenol (\( C_6H_5OH \)) is calculated as follows:
\[
\text{Molar mass of phenol} = 6 \times 12 + 5 \times 1 + 16 = 94 \, \text{g/mol}
\]
Now, calculate the number of moles of phenol in 4.7 g:
\[
\text{Moles of phenol} = \frac{\text{Mass of phenol}}{\text{Molar mass of phenol}} = \frac{4.7}{94} = 0.05 \, \text{mol}
\]
Step 2: Use the given yield to find the moles of X.
The reaction gives 60% yield of X. Therefore, the moles of X formed will be 60% of the moles of phenol:
\[
\text{Moles of X} = 0.05 \times \frac{60}{100} = 0.03 \, \text{mol}
\]
Step 3: State the final answer.
Hence, the number of moles of X formed is:
\[
\boxed{3 \times 10^{-2}} \, \text{mol}
\]