Between the two outer plate, there are two regions with different electric field. One is outside capacitor B, the electric field is from capacitor A only (we name it as region 1). And another one is inside capacitor B, the electric field is from both capacitors (we name it as region 2).Let d become the distance between plates of capacitor B. So region 2 has width of d, and region 1 also has width of d. And if A is area of the plates, C will equal to:

Because the capacitors are in series, they have same charge, Q. So we can say that electric field in region 2 is twice of electric field in region 1.
We know that electric field between two plates of a capacitor is , so electric fields in region 1 and region 2 are:

Therefore, the voltage between capacitor A's plates is:

And the voltage between capacitor B's plates is:

The total voltage is sum of these two voltage.

So the total capacitance is:

That's my solution.
If you have any question, correction, or comment, please leave a comment below.
Thank you.

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