Explanation:
Box 1: Microsoft Purview Data Map
For the searchable data catalog, use:
Provide a single searchable catalog of the data in all the databases. The catalog must contain metadata of the data. The solution must minimize storage requirements.
The Microsoft Purview Data Map provides the foundation for data discovery and data governance. It captures metadata about data present in analytics, software-as-a-service (SaaS), and operational systems in hybrid, on-premises, and multicloud environments.
Box 2: Azure Synapse Analytics
Provide a central data lake that contains specific data from multiple databases. The solution must include a big data engine that can create machine learning models.
Reference:
https://learn.microsoft.com/en-us/purview/data-map
https://learn.microsoft.com/en-us/purview/microsoft-purview-connector-overview
https://learn.microsoft.com/en-us/azure/architecture/data-guide/scenarios/data-lake

Azure Cosmos DB is a multi-model globally distributed NoSQL database. Cosmos DB stores data in atom-record-sequence (ARS) format. It unites under one roof several data management systems and exposes them as APIs. You can select between the Core (SQL) API and MongoDB API (document model), Cassandra API (column-oriented model), Gremlin API (graph model), and Table API (key-value model).
Azure CosmosDB provides high availability in two primary ways: replication data across regions and storing four copies of the data in a region. By default, Azure CosmosDB is distributed in all Azure regions. You can change the number of regions in your CosmosDB account. Suppose you associate five Azure regions with your data, and every region will have four copies of the data.
There will be twenty copies of your data available to use.
Reference:
https://docs.microsoft.com/en-us/azure/cosmos-db/high-availability

Explanation:
Data Warehouse: Azure Synapse Analytics (formerly SQL Data Warehouse)
Azure Synapse Analytics is a massively parallel processing (MPP) data warehouse that can handle large amounts of data and provides a scalable solution for analytics.
Managed Serving Layer: Azure Analysis Services
Azure Analysis Services provides a fully managed platform-as-a-service (PaaS) solution for online analytical processing (OLAP) and data modeling. It is suitable for serving analytical models to thousands of end users.