  We theoretically evaluate the feasibility to form magnetically-tunable
Feshbach molecules in collisions between fermionic $^6$Li atoms and bosonic
metastable $^{174}$Yb($^3$P$_2$) atoms. In contrast to the well-studied
alkali-metal atom collisions, collisions with meta-stable atoms are highly
anisotropic. Our first-principle coupled-channel calculation of these
collisions reveals the existence of broad Feshbach resonances due to the
combined effect of anisotropic-molecular and atomic-hyperfine interactions. In
order to fit our predictions to the specific positions of
experimentally-observed broad resonance structures \cite{Deep2015} we optimized
the shape of the short-range potentials by direct least-square fitting. This
allowed us to identify the dominant resonance by its leading angular momentum
quantum numbers and describe the role of collisional anisotropy in the creation
and broadening of this and other resonances.
