Can someone check this for me?

Question

Predict which reactions are spontaneous:
a) Zn(s) + 2H+(aq) --> Zn+2(aq) + H2(g)
b) CaCO3(s) + 2H2O(l) --> Ca(OH)2(s) + H2CO3(aq)
c) CH4(g) + O2(g) --> CO2(g) + 2H2O(g)
d) Ag+(aq) + Cl-(aq) --> AgCl(s)

I said a) and c) were spontaneous, based on phase changes/delta-s. Does that seem correct?

I'm not quite sure how your rule works with phase changes/delta s.
a is spontaneous. (What if I had written Cu(s) + 2H^+(aq)==>Cu^+2 + H2(g). That is not spontaneous but it looks like the same reaction, doesn't it?

b is not because CaCO3 is largely insoluble.
c is spontaneous IF (and it's a big if) we get over the activitation energy (which is usually done with a match or an electric spark). Something to initiate the reaction. But it won't happen without the initial help.
d is spontaneous for AgCl is a solid, the reactants are in solution.

a works because Zn metal is above H^+ in the activity series.
c works because the products have less energy than the reactants but that is essentially true for all spontaneous reactions. I may not know what your definition of spontaneous reaction is.
e works because an insoluble ppt is formed.