Anyone know the part number for the hose? For reference, it is the hose that connects to e-15-10 bottom right. I've tried looking, cannot find a part number. If that isn't possible. Does anyone know if fuel and emission hoses from autozone would work and what size fitting I should get? Once I replace it, should I bleed my cooling system? It's leaking all over my transmission linear solenoid assembly.

 

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It's either #4 or #5 on the link below since there are two e-15-10's in your provided depiction:
2006 TL:
Water Hose - 2006 Acura TL 4 Door SPORT (NAVI/SUMMERTIRE) KA 6MT (acurapartswarehouse.com)

 

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