How can I merge indices, such as converting a $4$-index list to $2$-index matrix, $C_{ijkl} \rightarrow D_{(ik); (jl)}$?

How can I merge indices, such as converting a $$4$$-index list to $$2$$-index matrix, $$C_{ijkl} \rightarrow D_{(ik); (jl)}$$? This example sometimes appears in physics applications.

Here, I mean $$(ik)$$ as a multi-index: if $$i$$ runs from $$1$$ to $$m$$ and $$k$$ runs from $$1$$ to $$n$$, then $$(ik)$$ runs over $$n*m$$ values from $$1,1$$ to $$n,m$$. That is, $$(i,k)$$ is ordered going like $$(1,1), (1,2)...(1,m), (2,1),(2,2)...(2,m),...(n,m)$$

To clarify what I mean, here is an example input and output.

[In]: a = Table[i*j*(k + 1)*l, {i, 1, 2}, {j, 1, 2}, {k, 1, 2}, {l, 1, 2}];
FourIndtoTwoInd[a]

[Out]: {{2,4,4,8}, {3,6,6,12}, {4,8,8,16}, {6,12,12,24}}


For example, the first row has values $${2,4,4,8}$$, corresponding to $$i,k=(1,1)$$ and $$j,l = (1,1), (1,2), (2,1), (2,2)$$.

You may use Flatten level combining syntax.
Flatten[a, {{2, 3}, {1, 4}}]

{{2, 4, 4, 8}, {3, 6, 6, 12}, {4, 8, 8, 16}, {6, 12, 12, 24}}