Showing that the class of regular languages are closed under merging / modified shuffle Consider $ab$ and $cd$ which are two words. We merge these two into 6 possibilities: $abcd, acbd, acdb, cabd, cadb, cdab$

So in general, a merge of words/sequences $x, y ∈ Σ∗$ , is a word of length $|x| + |y|$ with both $x$ and $y$ as disjoint subsequences in it.

For two languages $L1$ and $L2$ their merge is defined as the set of all possible merges of two words $x ∈ L1, y ∈ L2$.

So basically, a merge is a modified shuffle and should be of length that of the sum of the length of two languages, and should also be in order (see $ab$ and $cd$ example, as $b$ could not come before $a$).

I was thinking of just connecting the states of all $L1$ and $L2$ but this seems wrong as if you connect them all like a fully connected graph, one can jump and go back which is not acceptable. 

What's a basic idea on the construction I could do to prove this?
Express the two languages as NFA.  Use a product construction.  Think carefully about what transitions should exist in the product automaton.