Why is this method of solving this capacitor problem wrong? 
The problem was to solve for the capacitance of this system if initial capacitance was C.
I solved it using the method which has been given as wrong.My question is that why is potential difference across dielectrics 2 and 4 not same? Since the dielectrics 2 and 4 are between a metal plate and dilectric slab (k=6) covering entire width of the capacitor shouldn't the potential difference across them be the same(if the capacitor is disconnected)? Also does the answer depend on whether the capacitor is disconnected or not? Any hints would be appreciated, Thanks.
Edit: I think my assumption that charges won't redistribute if capacitor is disconnected is wrong, please correct me if I'm wrong.
 A: The potential across the middle line is not the same on both sides of the left hand capacitor which is implied in your right hand diagram.  
You can show this difference in potential using you middle diagram and assuming that you have 2 sets of capacitors each set being in series (and then connected together in parallel).
A: $\def\Eul{E_{\rm ul}} \def\Eur{E_{\rm ur}} \def\Ell{E_{\rm ll}} \def\Elr{E_{\rm lr}} \def\Kul{K_{\rm ul}} \def\Kur{K_{\rm ur}} 
\def\Kll{K_{\rm ll}} \def\Klr{K_{\rm lr}}$
Strictly speaking both solutions are wrong. I'm going to prove this, but I need a notation change. There are 4 regions within capacitor, which I'll call


*

*upper left (ul)

*upper right (ur)

*lower left (ll)

*lower right (lr).


Dielectric constants will be denoted accordingly: $\Kul$, $\Kur$, $\Kll$, $\Klr$. In old notations these were, in order, $K_3$, $K_3$, $K_1$, $K_2$. I'll also assume that lower plate is grounded and
upper plate has potential $V$.
Consider now the central solution. The electric fields are assumed uniform within each region. They are determined by the following equations
$$\Kul \Eul =  \Kll \Ell \qquad \Kur \Eur = 
\Klr \Elr$$
$$d\,(\Eul + \Ell) = V$$
$$d\,(\Eur + \Elr) = V.$$
But there are further conditions to be satisfied, deriving from electrostatic field being conservative:
$$\Eul = \Eur \qquad \Eul = \Eur$$
and it's easy to see that the latter equations are conflicting with the former.
Assume instead that the right method is ok i.e. the surface midway is equipotential and call $V'$ its potential. Then eqs. (1), (4) are still valid, whereas eqs. (2), (3) are replaced by 
$$\Ell = \Elr = V'/d \qquad \Eul = \Eur = 
(V - V')/d.\tag5$$
Again, the set of eqs. (1), (4), (5) is inconsistent.
Then how can we come out of it?
Although you didn't say it in the problem statement it's customary (and usually left implied) that a plane capacitor is much wider than thick, so that fringe effects are negligible. It's generally assumed that electric field is zero outside capacitor and uniform within. This can't really happen as such a field is not conservative, but is an acceptable approximation, because the involved volume is small.
In our case, with a composite dielectric, a fringe effect is also expected at the separation surfaces in between. If the capacitor is thin it's understandable that these fringe effects too are neglected, assuming (as I'd already said) uniform fields within each region. 
Again this is inconsistent with a conservative field, so that we must neglect the first of eqs. (5) (the second is ok, as the dieletric is the same in upper left and right regions). Then the central solution is obtained.
