Their are 4 C-H bonds in methane.
Given that the dissociation energy of methane is 360 kcal/mol so, that the dissociation energy of each C-H bond would be :
360/4 kcal/mol = 90 kcal/mol
​In ethane their are 6 C-H bonds and one C-C bonds.
Total bond dissociation energy of C-H bond is given by:
90 kcal/mol x 6 = 540 kcal/mol
​So, bond dissociation energy of C-C bond would be:
Total bond dissociation energy of ethane - ​Total bond dissociation energy of C-H bond
= 620 kcal/mol (given) - 540 kcal/mol
= 80 kcal/mol