Explanation:

Correct answer is (d). 

Possibility 1. 
As soon as we ended up learning why hair turns gray and discovering the identity of the cell that directly gives rise to hair, this project was started in an effort to understand how certain kinds of tumors form.
We can evidently observe here that though the first half of the above construction makes sense, the other half is absolutely absurd and irrelevant in the context. This eliminates options A and C.
Possibility 2.
In spite of this project was started in an effort to understand how certain kinds of tumors form, we ended up learning why hair turns gray and discovering the identity of the cell that directly gives rise to hair.
The above formation is grammatically incorrect.
Explanation:
‘In spite of’, ‘despite’ and ‘although’ are all used to show a contrast but there are differences in the structures used with them.
In spite of / despite
After in spite of and despite we use a noun or a pronoun.
Ex. We enjoyed our camping holiday in spite of the rain.
Ex. Despite the pain in his leg he completed the marathon.
Ex. Despite having all the necessary qualifications, they didn’t offer me the job.
Although
After although we use a subject and a verb.
Ex. We enjoyed our camping holiday although it rained every day.
Ex. Although he worked very hard, he didn’t manage to pass the exam.
Ex. The holiday was great although the hotel wasn’t very nice.
This hence eliminates option B as well.
Possibility 3.
Although this project was started in an effort to understand how certain kinds of tumors form, we ended up learning why hair turns gray and discovering the identity of the cell that directly gives rise to hair.
Clearly, the above synthesis is both grammatically and contextually correct and keeps the flow intact.
Option D is hence the correct answer.