  We exploit the $6D, {\cal N}=(1,0)$ and ${\cal N}=(1,1)$ harmonic superspace
approaches to construct the full set of the maximally supersymmetric on-shell
invariants of the canonical dimension ${\bf d=12}$ in $6D, \,{\cal N}=(1,1)$
supersymmetric Yang-Mills (SYM) theory. Both single- and double-trace
invariants are derived. Only four single-trace and two double-trace invariants
prove to be independent. The invariants constructed can provide the possible
counterterms of ${\cal N}=(1,1)$ SYM theory at four-loop order, where the first
double-trace divergences are expected to appear. We explicitly exhibit the
gauge sector of all invariants in terms of ${\cal N} = (1, 0)$ gauge
superfields and find the absence of ${\cal N}=(1,1)$ supercompletion of the
$F^6$ term in the abelian limit.
