  A new color basis system and confinement mechanism for multi-quark systems
are proposed according to the string-type picture of QCD. The color string
configurations in the strong coupling QCD are implemented in the set of color
basis states. The extended color Hilbert space for $QQ\bar Q\bar Q$ systems
includes a ''hidden color'' state, which mixes with two-meson states $Q\bar
Q+Q\bar Q$, This mixing effect leads to an attractive potential sufficient to
form a bound state. We apply a realistic Hamiltonian model with the new scheme
to fully charmed tetraquark states, $cc\bar c\bar c$, and find a bound and two
resonant states, which could potentially correspond to the $cc\bar c\bar c$
tetraquark candidates recently observed in experiments.
