Hi Seyed,

palindromic means reads the same both forwards and backwards so your cut site GGATCC on one strand 5' to 3' will read GGATCC on the other strand of the dna.

Asymmetric cutting means that the single stranded dna overhangs on the ends of the cut dna strands will not be the same.  So if the cut site was CCGG a symmetrical cut would give one fragment ending CC and the other ending GG but an asymmetric cut between the 2 Cs would give one dna fragment ending with a C but the other ending with a CGG. In your case cutting GGATCC will give strands nnnG        GATCCnn

                                                                                                nnnCTAG           Gnnn

The reason these are sticky end is that the GATC on the top strand has homology with the CTAG on the bottom strand so they will tend to anneal ,or stick, to each other . Blunt end cutters (,symmetrical cutters), have no single strand to anneal to each other so will not be described as sticky

Hi

Palindromic means both the complementary and non-complementary DNA strands are read same both forward or reverse.