= Solution
For a cubic phase, $d_{hkl}=a/\sqrt{h^2+k^2+l^2}$ and <Bragg's law> gives
$$
\sin^2\theta=\frac{\lambda^2}{4a^2}(h^2+k^2+l^2).
$$
The first six FCC-allowed squared-index sums are $3,4,8,11,12,16$, from indices all odd or all even. \b[The labels1–6 are therefore]
$$
\boxed{111,\quad200,\quad220,\quad311,\quad222,\quad400.}
$$
Remember that the plot reports $2\theta$, not $\theta$. The first peak gives
$$
a_{111}=\frac{\sqrt3(0.1542)}{2\sin(43.1^\circ/2)}
\simeq0.36356\,\mathrm{nm}.
$$
The last peak provides an independent estimate,
$$
a_{400}=\frac{4(0.1542)}{2\sin(115.9^\circ/2)}
\simeq0.36386\,\mathrm{nm}.
$$
Thus \b[$a\simeq0.3638\,\mathrm{nm}$] is appropriate to the supplied precision. The two estimates differ by about $0.08\%$; high-angle data are less sensitive to a fixed angular error, so the $400$ estimate is useful for the composition calculation. The printed angles do not justify many more significant figures or an exact fit of all six positions.
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