$L_1=\{a^nb^mc^{n+m}\; :\; m,n\geq1\}$ is Context-free language
(push $a's$ into stack, then push $b's$ into stack , read $c's$ and pop $b's$ , when no $b's$ left on stack, keep reading $c's$ and pop $a's$ , when no c's left in input , and stack is empty, then accepted).
$L_2=\{a^nb^nc^{2n}\; :\; n\geq1\}$ is Context-sensitive language and not context-free. (cannot implemented by one stack)
So, answer is option B.