Azure Data Factory is the correct choice for ingesting data from multiple on premises systems and cloud sources into Azure Synapse Analytics.

Azure Data Factory is a fully managed data integration service that includes built in connectors for databases, files, message stores and cloud services and it provides the Copy Activity and pipelines to move and transform data at scale into Synapse.

Azure Data Factory supports a self hosted integration runtime to securely connect to on premises systems and it can orchestrate scheduled and event driven pipelines so teams can centralize ingestion into Azure Synapse Analytics.

Azure Event Hubs is a high throughput streaming platform and event ingestion service and it is intended for telemetry and real time event streams rather than for orchestrated, connector based bulk data movement into Synapse.

Power BI is a business intelligence and reporting tool for visualization and analysis and it does not provide the pipeline orchestration and broad source connectivity needed to perform enterprise data ingestion into Synapse.

Azure Databricks is an analytics and data processing platform that is excellent for transformations and machine learning and it can read and write data to Synapse but it is not primarily a managed data integration service for connecting many on premises systems and orchestrating bulk loads.

Full AWS Practitioner Certification Question