Building an inventory chatbot on WhatsApp using FastAPI, Twilio's WhatsApp messaging API, Pyngrok, and SQLAlchemy requires several steps. First, set up a PostgreSQL database with the necessary schema and populate it with products. Then, configure the Twilio sandbox for WhatsApp and create a FastAPI backend to interact with the Twilio API. Use Ngrok to expose the FastAPI app to the public internet and authenticate the Twilio account. Finally, add chatbot logic to the /message endpoint to respond to incoming messages from clients, checking if the product is available in the inventory and updating its amount accordingly. The chatbot can be tested with various inputs to verify its functionality.