= Solution
On shell, a massless $\mathcal N=1$ <vector multiplet> contains a <gauge boson> with two transverse polarizations and a <gaugino> with two fermionic states. A <chiral superfield> contains a <complex scalar field>, hence two real bosonic states, and a <Weyl spinor> with two fermionic states. Their total is $4$ bosonic and $4$ fermionic states.
Suppose charged <scalar fields> acquire <vacuum expectation values> at a <supersymmetric vacuum>, where <F-flatness> and <D-flatness> hold. For each broken generator of the <gauge symmetry>, the <supersymmetric Higgs mechanism> combines one massless <vector multiplet> and one <chiral superfield> into a <massive N=1 vector multiplet>. The <gauge boson> absorbs one real <Goldstone boson>, acquiring its third polarization. The other real <scalar field> remains physical. The <gaugino> and the relevant <higgsino> mix into the four fermionic states. Thus the spin content is
$$
\boxed{(1,\tfrac12,\tfrac12,0),\qquad n_B=3+1=4,quad n_F=2+2=4}.
$$
Unbroken <supersymmetry> gives all these states the same mass through <supersymmetric mass degeneracy>. Remaining massive <chiral superfields> instead have spin content $(1/2,0,0)$, with two fermionic and two bosonic states of a common mass. The <auxiliary fields> ensure matching off shell but are not additional propagating particles in these counts.
The <super-Higgs mechanism> occurs when local <supersymmetry> is spontaneously broken in <supergravity>. Its spin-$3/2$ gauge field, the <gravitino>, absorbs the spin-$1/2$ <goldstino>:
$$
\boxed{2\text{ massless gravitino states}+2\text{ goldstino states}
\longrightarrow4\text{ massive gravitino states}}.
$$
The extra states have <helicities> $\pm1/2$, supplementing $\pm3/2$. The ordinary <supersymmetric Higgs mechanism> can preserve <supersymmetry> while breaking the internal <gauge symmetry>; the <super-Higgs mechanism> breaks the local <supersymmetry> itself. Spontaneously broken global <supersymmetry> leaves a physical massless <goldstino>, because there is no dynamical <gravitino> to absorb it.
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