refer to answer here:
Historically, both EUI-48 and MAC-48 were concatenations of a 24-bit OUI (Organizationally Unique Identifier) assigned by the IEEE and a 24-bit extension identifier assigned by the organization with that OUI assignment (NIC). The subtle difference between EUI-48 and MAC-48 was not well understood; as a result, the term MAC-48 is now obsolete and the term EUI-48 is used for both (but the terms “MAC” and “MAC address” are still used).
In other words, EUI-48 and the MAC number of a device represent the same thing! Usually it is represented in 12 hex (e.g. 0023.a34e.abc9), equivalent to 48 bits or 6 bytes.
By implementing the EUI-64 (64-bit Extended Unique Identifier format), a host can automatically assign itself a unique 64-bit IPv6 interface identifier without the need for manual configuration or DHCP. So it’s an IPv6 matter. Anyway, if you are interested about how it’s calculated, it is applied to a MAC address like this:
The 48-bit MAC address is split in half, the hex group
FFFE is inserted in the middle (after the 24th bit), and the seventh bit is inverted.
The MAC address 0021.86b5.6e10 (48 bit) becomes the EUI-64 address 0221.86ff.feb5.6e10 (64 bit)