  The ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction plays a key
role in the evolution of stars with masses of $M >$ 0.55 $M_\odot$. The
cross-section of the ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$
reaction within the Gamow window ($E_\textrm{c.m.}$ = 300 keV, $T_\textrm9$ =
0.2) is extremely small (about $10^{-17}$ barn), which makes the direct
measurement in a ground-based laboratory with existing techniques unfeasible.
Up until now, the cross-sections at lower energies can only be extrapolated
from the data at higher energies. However, two subthreshold resonances, located
at $E_x$ = 7.117 MeV and $E_x$ = 6.917 MeV, make this extrapolation more
complicated. In this work, the 6.917 MeV subthreshold resonance in the
${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction was investigated
via the
${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^{7}\mathrm{Li}){}^{16}\mathrm{O}$
reaction. The experiment was performed using the Q3D magnetic spectrograph at
the HI-13 tandem accelerator. We measured the angular distribution of the
${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^{7}\mathrm{Li}){}^{16}\mathrm{O}$
transfer reaction leading to the 6.917 MeV state. Based on the FRDWBA analysis,
we derived the asymptotic normalization coefficient (ANC) of the 6.917 MeV
level in $^{16}$O to be (1.10 $\pm$ 0.29) $\times 10^{10}$ fm$^{-1}$, with
which the reduced $\alpha$ width was computed to be $18.0\pm4.7$ keV at the
channel radius of 6.5 fm. Finally, we calculated the astrophysical
$S_{E2}(300)$ factor of the ground-state transitions to be 46.2 $\pm$ 7.7 keV
b. The result for the astrophysical $S_{E2}(300)$ factor confirms the values
obtained in various direct and indirect measurements and presents an
independent examination of the most important data in nuclear astrophysics.
