  The Method of Moments is a powerful framework to disentangle the relative
contributions of amplitudes of a specific process to its various phase space
regions. We apply this method to carry out a fully differential analysis of the
Higgs decay channel $h \to 4\ell$ and constrain gauge-Higgs coupling
modifications parametrised by dimension-6 effective operators. We find that
this analysis approach provides very good constraints and minimises
degeneracies in the parameter space of the effective theory. By combining the
decay $h \to 4\ell$ with higgs-associated production processes, $Wh$ and $Zh$,
we obtain the strongest reported bounds on anomalous gauge-Higgs couplings.
