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Number of ways in which 'n' identical items can be distributed among 'r' groups is $\binom{n+r-1}{r-1}$

5 blue pens (assumed identical) can be distributed among 6 boys in $\binom{5+6-1}{6-1}$ = 252 ways

6 black pens (assumed identical) can be distributed among 6 boys in $\binom{6+6-1}{6-1}$ =462 ways

Using multiplication rule of counting, 5 blue pens and 6 black pens can be distributed among 6 boys in 252*462 = 116424 ways.