Palindromic nucleotide sequences on DNA read same either we read from 5′ to 3′ or 3′ to 5′ direction. This means restriction enzymes read them from both sides which increases the chance of action of restriction enzyme to cut DNA strand.
The recognition site of restriction endonuclease is a far away from the center of palindromic sites, but they cut b/w the same base/pairs of DNA strand and leaves sticky overhang end for the action of DNA ligase so presence of palindromic site promote the action of restriction endonuclease for the formation of r-DNA.