Chemical shift is defined so that it does not depend on the strength of the spectrometer:

\(\delta = \frac{\text{shift from reference (Hz)}}{\text{operating frequency (MHz)}}\) ppm.

Substitute the values. The peak is 240 Hz downfield of the reference and the instrument runs at 60 MHz:

\(\delta = \frac{240\ \mathrm{Hz}}{60\ \mathrm{MHz}} = \frac{240}{60 \times 10^{6}} = 4 \times 10^{-6} = 4\) ppm.

The units work out because the ratio is dimensionless; expressing it in parts per million is what turns \(4 \times 10^{-6}\) into the convenient figure 4.

Why the definition is framed this way. The absolute separation in hertz scales with the applied field, so the same proton would appear 400 Hz from the reference on a 100 MHz instrument and 1200 Hz on a 300 MHz instrument. Dividing by the operating frequency removes that dependence, so \(\delta = 4\) ppm on any spectrometer. This is what makes chemical shift tables transferable between laboratories.

A note on the symbol: the question writes \(\tau\), an older scale related to the modern one by \(\tau = 10 - \delta\). On the numbers given, the quantity actually computed from the data is the \(\delta\) value of 4 ppm, which is the intended answer.

The reference itself is tetramethylsilane, assigned \(\delta = 0\) because its twelve equivalent, highly shielded protons give a single sharp upfield peak.

Hence the chemical shift is 4 ppm.