  Hypernuclei $ ^4_Y He$, $ ^4_Y H$, $ ^4_{YY} He$, $ ^4_{YY} H$, where
$Y=\Lambda$, $\Sigma_0$, $\Sigma_+$, $\Sigma_-$, A=4 are considered using the
relativistic twelve-quark equations in the framework of the dispersion relation
technique. Hypernuclei as the systems of interacting quarks and gluons are
considered. The relativistic twelve-quark amplitudes of hypernuclei, including
$u$, $d$, $s$ quarks are constructed. The approximate solutions of these
equations are obtained using a method based on the extraction of leading
singularities of the amplitudes. The poles of the multiquark amplitudes allow
us to determine the masses of hypernuclei with the atomic (baryon) number
$A=B=4$. The mass of state $ ^4_{\Lambda}He$ with the isospin projection
$I_3=1/2$ and the spin-parity $J^P=0^+$ is equal to $M=3922\, MeV$. The mass of
$ ^4_{\Lambda\Lambda}H$ $M=4118\, MeV$ with the isospin projection $I_3=0$ and
the spin-parity $J^P=0^+$ is calculated. We predict the mass spectrum of
hypernuclei with A=4, which is valuable to further experimental study of the
hypernuclei.
