This work consists of the first detailed photometric study of Terzan 6, one of the least known globular clusters in the Galactic bulge. Through the analysis of high angular resolution and multi-wavelength data obtained from adaptive optics corrected and space observations, we built deep, optical and near-infrared color-magnitude diagrams reaching ~4 magnitudes below the main-sequence turnoff. Taking advantage of 4 different epochs of observations, we measured precise relative proper motions for a large sample of stars, from which cluster members have been solidly distinguished from Galactic field interlopers. A non-canonical reddening law (with R_V_=2.85) and high-resolution differential reddening map, with color excess variations up to {delta}E(B-V)~0.8mag, have been derived in the direction of the system. According to these findings, new values of the extinction and distance modulus have been obtained: respectively, E(B-V)=2.36+/-0.05 and (m-M)_0_=14.46+/-0.10 (corresponding to d=7.8+/-0.3kpc). We also provide the first determinations of the cluster center and projected density profile from resolved star counts. The center is offset by more than 7-arcsec to the east from the literature value, and the structural parameters obtained from the King model fitting to the density profile indicate that Terzan 6 is in an advanced stage of its dynamical evolution, with a large value of the concentration parameter (c=1.94_-0.26_^+0.24^) and a small core radius (r_c_=2.6_-0.7_^+0.9^-arcsec). We also determined the absolute age of the system, finding t=13+/-1Gyr, in agreement with the old ages found for the globular clusters in the Galactic bulge. From the re-determination of the absolute magnitude of the red giant branch bump and the recent estimate of the cluster global metallicity, we find that Terzan 6 nicely matches the tight relation between these two parameters drawn by the Galactic globular cluster population.