= Solution
Treat the quoted maximum as the resonant <Z boson> contribution described by the <Breit-Wigner resonance cross section>. The <Electron> and <Positron> each have <spin> $1/2$, while the <Z boson> has <spin> one, so
$$
g=\frac{2(1)+1}{[2(1/2)+1]^2}=\frac34.
$$
Neglect the <electron mass> at this <centre-of-mass energy>. Each incident momentum magnitude is then $p_i=E_0/2$ in <natural units>. Write $B_e=\Gamma_{ee}/\Gamma$. At the resonance peak the denominator is $\Gamma^2/4$, and the same partial <decay width> appears for production and decay:
$$
\sigma_{\rm peak}=\frac{\pi g}{p_i^2}\frac{\Gamma_{ee}^2}{\Gamma^2/4}
=\frac{12\pi}{E_0^2}B_e^2.
$$
The <peak resonance cross section and branching fractions> relation contains $B_e^2$, because the electronic channel occurs at both ends of the resonant process.
For an area in ordinary units, restore $(\hbar c)^2$. The original PDF prints $\hbar c=197.5\,\mathrm{MeV}$, which is dimensionally incomplete: the intended standard conversion is $197.5\,\mathrm{MeV\,fm}=0.1975\,\mathrm{GeV\,fm}$. Also,
$$
2.0\,\mathrm{nb}=2.0\times10^{-37}\,\mathrm{m^2}
=2.0\times10^{-7}\,\mathrm{fm^2}.
$$
Consequently
$$
B_e=\sqrt{\frac{\sigma_{\rm peak}E_0^2}{12\pi(\hbar c)^2}}
=\sqrt{\frac{(2.0\times10^{-7})(91.2)^2}{12\pi(0.1975)^2}},
\qquad
\boxed{B(Z^0\to e^+e^-)=0.03363\simeq3.4\%.}
$$
This estimate uses the supplied resonance model. The full physical elastic <Electron>-<Positron> cross section also contains nonresonant <photon> exchange and interference; an experimental use of the formula must isolate the resonant contribution.
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