Hdmi cables honestly dont like bending too much around the ends so attach to the cable use masking tape on the head of the cable so you dont get dust in it and manually feed the hdmi and the draw wire into the hole. Family handyman 234731 views.

Rocketfish 24 In Wall Hdmi Cable
How to fish hdmi cable through wall. Carefully extend the fish tape from one opening to the other. Your buddy attaches the cable to the pull cord and you pull it back down with the cable. Fit the wall gang boxes in the holes. That way you should avoid any timbers in your walls. Keep feeding the hdmi as you pull on the exit line and bring it out. Tape the end of the fish tape tightly onto the cable with electrical tape.
If you need to fish a larger cable or bundle or if your buddy is going to feed the cable to you from above or below thread a pull cord through the bull nose. Then retract the fish tape to pull the cable through. Push the rod to the same corner you used with the drill bit. The wall is heavily insulated and the fish tape has caught several times. Carefully push the top low voltage box into the wall cavity just enough that you can easily access the tube from the bottom hole. Then you would loosen the screws that tighten the wings of the box and and gently pull the box out of the wall you may have to push in on the box as you turn the screw to get the wing to free up from the back of the wall.
How to fish wire and cable through a finshed wall duration. Push the cables a little into the the wall through the box so there is slack cable in the wall cavity. The rod will follow the corner and pass through the hole the bit made. Make sure the tape is smooth so the cable can slide through the opening. Use existing cable as a pull you need to add one data cable to an existing work area location. Feed the wire fishsnake wire through the top hole down through the wall and fish it out through the bottom hole.
You dont need to tighten them down yet. Extend the fish stick so that it protrudes out of both the top and bottom holes and you can tape it to the wall temporarily. It probably wont so do some fine tuning and shave away areas that need it. Push the fish stick up through the tube and out of the top low voltage box. Pull the cable through with a fish tape. You have been fishing in the wall for 45 minutes where you need to drop the cable and your patience is running thin.
How to hide tv cables in the wall low voltage hdmi cat5 speaker wires duration.