[Rutherford]

The problem is attached.

The alkyne proton is more acidic than the alkene one, so it has a bigger chemical shift. H1 is near -OH, so it would have a big chemical shift. H3 doesn't have any special feature, so I would order them: 3<4<2<1. Is this correct?

[SinkingTako]

The alkyne proton is more acidic than the alkene one, but it does not mean that it has higher shift. Acidity and how shielded the proton is are 2 different concepts. Acidity is based on like the atom, resonance, inductive effect and orbital type. So in a sense the effects are similar to the factors affecting shift. But acidity examines the charge dispersion on the conjugate base, not the charge dispersion on the proton (which is what NMR is looking for). Additionally,  NMR is weird and is affected by magnetic anisotropic effects which are completely irrelevant to acidity.

So I'll rank H3<H2<H1<H4.
Alkyne shift is lower than alkene because of anisotropic effect, H1 is higher than H2 due to deshielding by O. Yup. I think so. Check the NMR table?

[Rutherford]

Thanks for clearing this up. I don't want to use an NMR table, because I want to logically deduce the answer.