In the question two statements are given, followed by three conclusions, I, II and III. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement:

1. Some doctors are engineers.
2. All engineers are lawyers.
Conclusion:

I. Some lawyers are doctors.
II. All lawyers are engineers.
III. Some engineers are doctors. ​​

Statement:

1. Some doctors are engineers.
2. All engineers are lawyers.

Conclusion:

I. Some lawyers are doctors. (True, some doctors are engineers and all engineers are lawyers, so that means some lawyers are doctors).
II. All lawyers are engineers. (False, all engineers are lawyers).
III. Some engineers are doctors. (True, some doctors are engineers, so that means some engineers are also doctors).

So, ​Both Conclusion I and III follows.

Thus, correct option is (b).