Option a) aabbaba
It start and end with a
$S\longrightarrow aS\longrightarrow aA$
now string end with a so we take $A\longrightarrow bAa$
$S\longrightarrow aS\longrightarrow aA\longrightarrow abAa$
as 'aa' in not formed at starting, option a is wrong.
Option b) aabaaba
It is starting with a and ending with a,
so same as above case 'aa' is not formed at starting, option b is wrong.
Option c) abababb
it is string starting with a and ending with b,
$S\longrightarrow aS\longrightarrow aA$
now string end with b so we take $A\longrightarrow aAb$
$S\longrightarrow aS\longrightarrow aA\longrightarrow aaAb$
as it has 'aa' in starting and we want 'ab' as the first two terminals,
option c is wrong.
Option d) aabbaab
it is string starting with a and ending with b,
$S\longrightarrow aS\longrightarrow aA$
now string end with a so we take $A\longrightarrow aAb$
$S\longrightarrow aS\longrightarrow aA\longrightarrow aaAb$
take $A\longrightarrow bAa$
$S\longrightarrow aS\longrightarrow aA\longrightarrow aaAb\longrightarrow aabAab$
take $A\longrightarrow bAa$
$S\longrightarrow aS\longrightarrow aA\longrightarrow aaAb\longrightarrow aabAab\longrightarrow aabbAaab$
$A\longrightarrow \epsilon$
$S\longrightarrow aS\longrightarrow aA\longrightarrow aaAb\longrightarrow aabAab\longrightarrow aabbAaab\longrightarrow aabbaab$
option d is correct.