  We perform a quantitative analysis of the decays of $cc\bar c\bar c$
tetraquarks with $J^{PC}=0^{++}, 2^{++}$ into 4 muons and into hidden- and
open-charm mesons and estimate, for the first time, the fully charmed
tetraquark decay width. The calculated cross section upper limit is $\sim 40$
fb for the 4 muons channel, and $\sim 28$ nb for the $D^{(*)} \bar D^{(*)} \to
e\mu$ channel. On the basis of our results, with the present sensitivity LHCb
should detect both signals, for $0^{++}$ and $2^{++}$ fully-charmed
tetraquarks.
