I'm trying to understand what is the sequence of apdu commands needed to communicate between the smart card and the reader in order to enroll a fingerprint.

This link explains the APDU communication protocol
https://en.m.wikipedia.org/wiki/Smart_card_application_protocol_data_unit

An APDU command consists of two parts: the Command APDU and the Response APDU. The Command APDU is sent from the card reader to the smart card and contains the command to be executed by the smart card. The Response APDU is sent from the smart card to the card reader and contains the response to the command.

I don't understand what sequence of commands need to be sent between STM32 board and NXP SPM60 smart card reader to enroll fingerprint.

There are multiple commands. Can any one tell me which sequence of command is required to send to NXP SPM60

 

Not without doing a whole lot of research... That page explains the physical communication in terms of bytes sent/received. The second and fourth links on that page give a list of commands that can be sent. But how you use them is not described here. Most systems provide a higher level user interface. But this link might tell you more.