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Inspired by the observation of the $X(6900)$ by LHCb and the $X(6600)$ (withmass $6552\pm 10$ $\pm 12$ MeV) recently by CMS and ATLAS experiments of theLHC in the di-$J/\Psi $ invariant mass spectrum, we systemically study massesof all ground-state configurations of the hidden heavy-flavor tetraquarks$q_{1}Q_{2}\bar{q}_{3}\bar{Q}_{4}$ and $Q_{1}Q_{2}\bar{Q}_{3}\bar{Q}_{4}$($Q=c,b$;$q=u,d,s$) contaning two and four heavy quarks in the MIT bag modelwith chromomagnetic interaction and enhanced binding energy. Consideringcolor-spin mixing due to chromomagnetic interaction, our mass computationindicates that the observed $X(6600)$ is likely to be the $0^{++}$ groundstates of hidden-charm tetraquark $cc\bar{c}\bar{c}$ with computed masses$6572$ MeV, which has a $0^{++}$ color partner around $6469$ MeV. The fullybottom system of tetraquark $bb\bar{b}\bar{b}$ has masses of 19685 MeV and19717 MeV for the the $0^{++}$ ground states. Further computation is given tothe tetraquark systems $sc\bar{s}\bar{c}$, $sb\bar{s}\bar{b}$,$cb\bar{c}\bar{b}$, $nc\bar{n}\bar{c}$ and $nb\bar{n}\bar{b}$, suggesting thatthe $Z_{c}(4200)$ is the tetraquark $nc\bar{n}\bar{c}$ with $J^{PC}=1^{+-}$.All of these tetraquarks are above their lowest thresholds of two mesons andunstable against the strong decays.

Mass spectra of hidden heavy-flavor tetraquarks with two and four heavy quarks