Final answer:
The creation, modification, and deletion of VLANs on the local switch can be performed in VTP Server mode and VTP Transparent mode.
Step-by-step explanation:
The two VTP (VLAN Trunking Protocol) modes that allow for the creation, modification, and deletion of VLANs on the local switch are the VTP Server mode and VTP Transparent mode.
In VTP Server mode, a switch can create, modify, and delete VLANs for the entire VTP domain. Any changes made on a server mode switch are propagated to all other switches in the VTP domain. Therefore, this mode is typically used in the core layer of the network where changes need to be frequently made and updated across all access switches.
Meanwhile, in VTP Transparent mode, a switch can create, modify, and delete VLANs, but these changes are only local to that switch and are not propagated throughout the VTP domain. This mode can be used when the network requires certain VLAN configurations that are unique to a particular switch and should not impact other switches in the network.