Is this the heater hose connector?

[Hispoohbear83]

We bought this last night. It’s an 05 explorer. Eddie Bauer edition. Drove it 15 miles home and this piece started spewing antifreeze 1 mile from home. Saw the leak from the crack. Needing to know if this is in fact the heater hose connector? What is the standard size barbed connector for a 5/8 hose? Any help appreciated. TIA

 

[Number4]

This is a flow restrictor for the heater core. If I recall, it’s $18 from the dealership or just replace it with a plastic splice. It’s a common failure point and I replaced it with the same part from the dealer.