  We present the identification of the COCONUTS-2 system, composed of the M3
dwarf L 34-26 and the T9 dwarf WISEPA J075108.79$-$763449.6. Given their common
proper motions and parallaxes, these two field objects constitute a physically
bound pair with a projected separation of 594$"$ (6471 au). The primary star
COCONUTS-2A has strong stellar activity (H$\alpha$, X-ray, and UV emission) and
is rapidly rotating ($P_{\rm rot} = 2.83$ days), from which we estimate an age
of 150-800 Myr. Comparing equatorial rotational velocity derived from the TESS
light curve to spectroscopic $v\sin{i}$, we find COCONUTS-2A has a nearly
edge-on inclination. The wide exoplanet COCONUTS-2b has an effective
temperature of $T_{\rm eff}=434 \pm 9$ K, a surface gravity of $\log{g} =
4.11^{+0.11}_{-0.18}$ dex, and a mass of $M=6.3^{+1.5}_{-1.9}$ $M_{\rm Jup}$
based on hot-start evolutionary models, leading to a $0.016^{+0.004}_{-0.005}$
mass ratio for the COCONUTS-2 system. COCONUTS-2b is the second coldest (after
WD 0806$-$661B) and the second widest (after TYC 9486-927-1 b) exoplanet imaged
to date. Comparison of COCONUTS-2b's infrared photometry with ultracool model
atmospheres suggests the presence of both condensate clouds and non-equilibrium
chemistry in its photosphere. Similar to 51 Eri b, COCONUTS-2b has a
sufficiently low luminosity ($\log{(L_{\rm bol}/L_{\odot})} = -6.384 \pm 0.028$
dex) to be consistent with the cold-start process that may form gas-giant
(exo)planets, though its large separation means such formation would not have
occurred in situ. Finally, at a distance of 10.9 pc, COCONUTS-2b is the nearest
imaged exoplanet to Earth known to date.
