If $L$ and $\bar L$ are recursively enumerable then $L$ is
$L$ is recursively enumerable means a $TM$ accepts all strings in $L$. $\bar L$ is recursively enumerable means a $TM$ accepts all strings in $\bar L$. So, we can always decide if a string is in $L$ or not, making $L$ recursive.
Recursively enumerable language is NOT Closed under complementation where as Recursive lang is Closed Under complementation .
Ans D) Recursive , is correct option.
@ Manu Thakur The logic is simple, If L is recursively enumerable, then the complement of L is recursively enumerable if and only if L is also recursive.For proof just see the best ans.Actually, this is one of the best methods to differentiate (or to check whether the lang is rec or rel) B/w Recursive language and Recursively Enumerable language.