Finding the private key in BB84 quantum cryptography
The first stage of the BB84 protocol involves throwing away any measurements where the measurements were performed with a different basis.  After throwing those away, we are left with the following binary sequence:

$$11 10 0 0 01 10 01.$$

However, in the BB84 protocol as it was originally published, this is not the final key.  There are several subsequent steps that are performed after this.

In the second stage, Alice and Bob check whether they both got approximately the same sequence, by comparing a randomly chosen subset of this sequence.  If there are too many errors (differences between Alice's string and Bob's string) in those randomly selected positions, then they declare it a failure and go back to the beginning and start over.

In the third stage, a privacy amplification protocol is applied to the remaining bits, to derive a key that Alice and Bob can use.

Consequently, in the real BB84 protocol, the final key is not $111000011101$.  That's just the output of the first stage.  The final key is the output of the third stage.

However, I don't know what they taught you in your class.  I'd hope that they taught you all three stages, but if they only taught you the first stage, then you'd get a different answer than if they taught you the full protocol.  Therefore, we can't really tell what the right answer to your exam might have been.  If you want to know about that, I suggest you contact your instructor.