in chess board we have 8 rows and 8 columns.
take a row and see how many ways you can choose 2 adjacent boxes. you can choose it in 7 ways.
example if there are boxes form 1 to 8, number of adj boxes =
(1,2)(2,3)(3,4)(4,5)(5,6)(6,7)(7,8) = 7
same happens with other 7 rows too. so from each row we can choose 2 adjacent boxes in 8*7 ways.
now, there can be boxes which share common edge beween the rows.
lets see how many adjacent boxes can be present in each column.
there will be 7 adj boxes in 1 column. so 8*7 adj boxes will be in all the columns.
so, total number of adj boxes= (8*7+8*7)C1
we are choosing 2 boxes from 64 boxes so 2*8*7/(64C2) = 1/18