Biggest tire I can put on factory 1968 Dart Rim

1- that’s not a factory rim for a ‘68 Dart, 13’s or 14’s only. Are they 5x4" or 5x4.5"?

2- by the tire manufacturer recommendations, the biggest for the front would probably be a 205/65/15. In the back, a 215/70/15 ( at 26.8" it's probably a little too tall for the front). Wider than that should have a 6" or wider rim, much taller than that will likely require a higher than stock ride height or other modifications.

3- a 5.5" wide rim will measure 6.5" from the outside lip to the outside lip, so make sure they're 5.5's and not 4.5's before you order tires.

Now cue all the guys that have run bigger tires than that, because of course they know more about tires than the tire manufacturers. Can you? Of course. Should you? Not according to the people that make the tires.