2001 Mitsubishi Eclipse 3.0L MFI 6cyl

“Why is the book showing a fireing order of 123456 and the cap showing 153426”

I’ve never seen a firing order listed on a distributor cap (it wouldn’t generally make sense since the same cap may be used in different applications with different firing orders). I’m guessing the number is just some sort of part number that just so happens to be six digits long and have all digits between 1 and 6 in it.

Have you tried hooking it up like the book says? Also, what book are you using-- I’ve known the haynes and chilton manuals to have the wrong firing orders or wrong engine rotation directions listed.

if you look at autozone.com and look up the cap you will see what i am talking about i would think if the firing order is 123456 the cap plug holes ould be in line just like the firing ordernot 135426

Look at the INSIDE of the distributor cap. You may see that the distributor rotor doesn’t spark to the terminal it points to. You may have to use an ohmmeter to trace the paths from the contact posts to the spark plug wire sockets.
See if it doesn’t work if you plug each spark plug wire into the cap as each socket is numbered on the cap.