The first photo is a rear view of the earlier, similar DMR-EZ47 (from the 2007 model year). The inputs and outputs are somewhat basic. Notice that the composite "DVD/VHS COMMON OUT" provides VHS and DVD signals while the composite "DVD PRIORITY OUT" provides only the DVD output.
While I have no familiarity with DirectTV receivers I would think that they have the usual set of outputs. This will include (digital) HDMI and (analog) component red, green, blue outputs for connection to a HDTV. The HDMI carries video and audio while the component connections carries only the video. When component outputs are used the white/red audio connections are also necessary. There will certainly be a composite video output, the yellow connection, and perhaps there will be a S-Video output, a round black connector with several pins. The composite video and S-Video both require use of the white/red audio outputs. Perhaps the DirectTV receiver might have a threaded RF coax cable output that carries the video and audio.
If more than a single set of white/red audio outputs are needed use "Y" adapters, as seen the second photo, to split the DirectTV receiver's single set of audio outputs.
Sometimes satellite receiver or cable box outputs are not "active." By this I mean that they may not be functional until one goes into a configuration menu to set the output to "ON" or "ENABLE" or "ACTIVATE" or some such term. That information should be in whatever instruction sheet or user guide was provided with the DirectTV receiver.