Markarian 6 is a nearby (D ~ 78 Mpc) Seyfert 1.5, early-type galaxy, with a double set of radio bubbles. The outer set spans ~7.5 kpc and is expanding into the halo regions of the host galaxy. We present an analysis of our new Chandra observation, together with archival XMM-Newton data, to look for evidence of emission from shocked gas around the external radio bubbles, both from spatially resolved regions in Chandra and from spectral analysis of the XMM-Newton data. We also look for evidence of a variable absorbing column along our line of sight to Mrk 6, to explain the evident differences seen in the active galactic nucleus (AGN) spectra from the various, non-contemporaneous, observations. We find that the variable absorption hypothesis explains the differences between the Chandra and XMM-Newton spectra, with the Chandra spectrum being heavily absorbed. The intrinsic N H varies from ~8 × 1021 atoms cm–2 to ~3 × 1023 atoms cm–2 on short timescales (2-6 years). The past evolution of the source suggests this is probably caused by a clump of gas close to the central AGN, passing in front of us at the moment of the observation. Shells of thermal X-ray emission are detected around the radio bubbles, with a temperature of ~0.9 keV. We estimate a temperature of ~0.2 keV for the external medium using luminosity constraints from our Chandra image. We analyze these results using the Rankine-Hugoniot shock jump conditions, and obtain a Mach number of ~3.9, compatible with a scenario in which the gas in the shells is inducing a strong shock in the surrounding interstellar medium (ISM). This could be the third clear detection of strong shocks produced by a radio-powerful Seyfert galaxy. These results are compatible with previous findings on Centaurus A and NGC 3801, supporting a picture in which these AGN-driven outflows play an important role in the environment and evolution of the host galaxy.