When you have a doublet of doublets how many neighboring Hydrogens will there be?

In the first order spectrum, for which I will add an illustration later, the given absorption is split into a doublet by coupling to the first proton, and this doublet is split into another doublet by coupling to the SECOND chemically non-equivalent proton. Sometimes these doublets overlap to give what seems to be an apparent triplet. Such so-called multiplets can be resolved by doing the experiment on a higher field instrument.

A doublet of doublets (dd) occurs when a hydrogen atom is coupled to two non-equivalent hydrogens.

An example is the NMR spectrum of methyl acrylate.

(From Chemistry LibreTexts)

Each of the vinyl protons #"H"_text(a), "H"_text(b)# and #"H"_text(c)# is a dd.

Let's examine the #"H"_text(c)# signal at 6.21 ppm.

There are four separate peaks because #"H"_text(c)# is coupled to both #"H"_text(a)# and #"H"_text(b)#, but with different coupling constants for each.

The result is a doublet of doublets.

The splitting diagram shows that #"H"_text(c)# is split into a doublet by #"H"_text(a)# with a large coupling constant #J_text(trans)#.

These peaks are each split into doublets by coupling with #"H"_text(a)# with a much smaller coupling constant #J_text(gem)# = 1.5 Hz.