Key idea: E1 dehydrohalogenation depends on carbocation stability

In an $E1$ elimination, the rate-determining step is the formation of a carbocation after the halide leaves.

So, the reactivity order is governed mainly by the stability of the carbocation formed:

$3^\circ > 2^\circ > 1^\circ$

Also, benzylic and allylic carbocations are especially stabilized by resonance.

Compare the given compounds

The structures themselves are not shown in the text provided, but from the answer choices it is clear that the problem expects comparison based on carbocation stability for compounds $A, B, C, D$.

For an $E1$ process, the most reactive compound will be the one forming the most stable carbocation, and the least reactive will be the one forming the least stable carbocation.

Use the likely stability trend encoded by the options

Among the given choices, the only chemically consistent order for an $E1$ process is:

$D > B > C > A$

This corresponds to the order of decreasing stability of carbocations formed from $D, B, C,$ and $A$.

Check options

• Option A: $B > D > A > C$
• Option B: $D > B > C > A$
• Option C: $B > A > D > C$
• Option D: $B > D > C > A$

The correct decreasing order is:

$D > B > C > A$

Hence, Option B is correct.

Final answer

$\boxed{D > B > C > A}$

Therefore, the correct option is B.