How did this problem lead to a roman victory at zama?

Because Hannibal had to slaughter majority of his horses in Italy, he was left with minimal cavalry, he also did not arrive in time to prevent Massinia and Scipius from joining up leaving him at the mercy him unable to choose the battleground. The elephants they unleashed towards the Roman ranks were also foiled by because the Roman formation just let the beasts pass through while confusing them with trumpets and pelting them with arrows. The Carthaginian army that Hannibal utilized lacked battle experience save for the army of 12,000-15,000 that arrived together with Hannibal from Rome.