Anyone who tries to change the system will have to 'reckon with' me. = Anyone who tries to change the system will have me to 'reckon with'. [=I will oppose/fight anyone who tries to change the system]
She 'was reckoned' [='considered'] to be among the group's leaders. = She 'was reckoned' as one of the group's leaders.
When he won his first three matches, the other players realized that he was 'a force/man to be reckoned with'.
(..) If I win, you do the road my way. Doc, what're you doin'? I don't mean to be rude here, but you probably go zero to sixty in, like, what? Three-point-five years? Then I reckon you ain't got nothin' to worry about. You know what, old-timer? That's a wonderful idea. Let's race. Gentlemen, (..)2006 Cars