The reaction which is a synthesis reaction is
BaO + CO₂→ BaCO₃
Explanation
Synthesis reaction a reaction which involve combination of two or more simple substance to from a more complex substance.
BaO and Co₂ combine to form BaCO₃ ( a more complex substance) therefore the reaction above a synthesis reaction.
CH₄ + O₂→ Co₂ +H₂O is a combustion reaction since it involve a hydrocarbon reacting with O₂
Both FeCo₃ → feO +CO₂ and 2NH₃ → 2N₂ + 3H₂ are decomposition reactions.