  This Letter presents a constraint on the total width of the Higgs boson
($\Gamma_H$) using a combined measurement of on-shell Higgs boson production
and the production of four top quarks, which involves contributions from
off-shell Higgs boson-mediated processes. This method relies on the assumption
that the tree-level Higgs-top Yukawa coupling strength is the same for on-shell
and off-shell Higgs boson production processes. The result is based on up to
140 fb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of
$\sqrt{s}$ = 13 TeV collected with the ATLAS detector at the Large Hadron
Collider. The observed (expected) 95% confidence level upper limit on
$\Gamma_H$ is 450 MeV (75 MeV). Additionally, considering the constraint on the
Higgs-top Yukawa coupling from loop-induced Higgs boson production and decay
processes further yields an observed (expected) upper limit of 160 MeV (55
MeV).
