  We have analyzed Chandra and Suzaku observations of the globular cluster
Terzan 6, made when the recurrent transient GRS 1747-312 was in quiescence. Our
analysis reveals the presence of a second eclipsing, bursting neutron-star
low-mass X-ray binary in the central regions of the cluster, in addition to GRS
1747-312. The new source, which we name Terzan 6 X2, is located only ~0.7
arcsec away from GRS 1747-312 in the 2021 Chandra images. The detection of a
5.14 ks-long eclipse in the light curve of X2 at a time not predicted by the
ephemeris of GRS 1747-312 confirms that it is an unrelated source. Using the
Suzaku light curve from 2009, which in addition to a type-I X-ray burst also
showed an eclipse-like feature, we constrain the orbital period to be longer
than 16.27 h. The 0.5-10 keV luminosities of X2 vary in the range of
~0.24-5.9x10^34 erg/s on time scales of months to years. We have identified a
plausible optical counterpart of X2 in HST F606W and F814W images. This star
varied by 2.7 mag in V_606 between epochs separated by years. In the cluster
color-magnitude diagram, the variable counterpart lies in the blue-straggler
region when it was optically bright, about 1.1-1.7 mag above the main-sequence
turn-off. From the orbital period-density relation of Roche-lobe filling stars
we find the mass-donor radius to be >0.8 Rsun.
