Explanation:

To automate the given language {a,b}*{aba}{a,b}*, we need to design a finite automaton that recognizes strings that start and end with any combination of 'a' and 'b', with 'aba' appearing somewhere in the middle.

States:
To design the automaton, we need to determine the number of states required. Let's consider the different parts of the language and determine the states needed for each part.

Part 1: {a,b}* - This part allows any combination of 'a' and 'b' before and after 'aba'. It requires at least 2 states to handle the initial and final states.

Part 2: {aba} - This part requires 3 states to handle the sequence 'aba'. Let's call these states q1, q2, and q3.

Part 3: {a,b}* - This part allows any combination of 'a' and 'b' after 'aba'. It requires at least 2 states to handle the initial and final states.

Total number of states:
Considering the states required for each part, we have:
- 2 states for part 1
- 3 states for part 2
- 2 states for part 3

Therefore, the total number of states required to automate the language {a,b}*{aba}{a,b}* is 2 + 3 + 2 = 7.

However, there is a redundant state in the automaton. The transition from the final state of part 1 to the initial state of part 2 can be combined into a single state, resulting in fewer states.

Reducing the number of states:
By merging the final state of part 1 and the initial state of part 2 into a single state, we can reduce the number of states to 6.

Final answer:
Hence, the correct answer is option 'A' (4 states) after reducing the redundant state, not option 'D' (6 states).