that connector thing is a lightning audio 0 to 4 gauge adapter so the audio line goes to the 4 gauge in on the terminal and the 0 gauge for the battery dist block goes into the 0 gauge. i'll tell u this. mine were a huge [censored] to do also. i actually dremeled out the 0 gauge on the terminal to increase the diameter to get the 0 gauge wire in and "shaved" some 0 gauge wire strands to get it more compact. i also dremeled the hole on the terminal where they sit on the battery post so the terminal would sit all the way down.i did it a hair too much. they are very slightly loose, but not enough to shake or slide around at all. maybe each car is different but i had to dremel alot out of the battery box to get the battery down and to the far left as much as possible. my neg terminal started to hit the hood slightly so i had to do some more dremeling to the box and needed to turn the terminals more counterclockwise to get the mass of the terminals away from the downward slope of the hood. there's a pos and neg dist block screwed into the back of the batt box. the stock wiring was a pain in the a$$ to get to fit right but its very doable. i can visibly see my inline fuse holder and easily change the fuse if it blows. its within 18 inches. i couldve put it dangling under the air box but then had to remove the airbox just to check if the fuse is blown and/or change. i wanted it to look good, be functional, and userfriendly. to prevent the battery from possibly sliding around, i got some pipe insulation wrapping tubing and cut it to fit into the open space to the right of the battery. there's 3 pieces used and each one has strips of the insulations stuffed into the middle of the tubing to make it more solid to hold the battery in place. the terminals plastic covers i keep on all the time. i drilled holes where the hex gold screws stick up so the covers can sit down on the terminals properly. so far everything has worked perfectly. it honestly took me about 3 days to get the right fit and finish. this included the wiper cowl removal, running the power wire, and lots of dremeling and trimming the wiring a little at a time. i cut out a slanted piece from the battery tie down to allow the 0 gauge to sit down and not get crushed, again, i had to turn the terminals for clearance. the hood grazes the neg plastic cover but nothing to creat a dimple. up next is upgrading the grounds to 0 gauge and running 0 gauge to the alt