To solve this logical reasoning problem, we need to identify the missing letters in the series: abb_abbcabbcabbca_bcabbca_bc_bbc. Let's analyze the pattern.

1. Observe the repeating pattern in the given series. The sequence can be broken down as follows: abb|_abbc|abbca|bbcabbca|_bc|abbc.
2. The repeating pattern appears to be "abbc". Let's check each segment to confirm this hypothesis:
   • The first complete segment is abbc.
   • The second segment abbca starts matching up to abbc and then breaks and starts again.
   • The sequence bbcabbca_bc continues with this suspected repetitive pattern, except for blank spaces.
3. Identify the blanks and fill them with "abbc" pattern to ensure continuous repetition:
   • The first blank is preceded by abb, suggesting it can be completed by an "c".
   • The second blank comes after a, suggesting a b to fit the potential continuity.
   • The third blank can logically be a to follow the sequence abbc continuously.
   • The last blank must be b to form the last segment bbcabbca.
4. This results in filling the blanks with cbb|a, forming a part of the series that completes as repeating abbc.
5. Matching options with the identified pattern:
   • cbba fits our sequence perfectly as deduced.
   • Other options like abcd, cdba, and aabb do not maintain the repetitive sequence and therefore do not fit.

Therefore, the correct option is cbba, which correctly completes the given sequence following the identified pattern.