Error:
Failed to commit the change on the object because access is denied. See inner exception for more information.

MapiExceptionNoAccess: Unable to create folder. (hr=0×80070005, ec=-2147024891)
Diagnostic context:
Lid: 18969 EcDoRpcExt2 called [length=73]
Lid: 27161 EcDoRpcExt2 returned [ec=0x0][length=148][latency=0]
Lid: 23226 — ROP Parse Start —
Lid: 27962 ROP: ropCreateFolder [28]
Lid: 17082 ROP Error: 0×80070005
Lid: 25953
Lid: 21921 StoreEc: 0×80070005
Lid: 27962 ROP: ropExtendedError [250]
Lid: 1494 —- Remote Context Beg —-
Lid: 26426 ROP: ropCreateFolder [28]
Lid: 21970 StoreEc: 0x8004010F PropTag: 0x668F0040
Lid: 31229 Error: 0×0
Lid: 1091 StoreEc: 0×80070005
Lid: 4975 StoreEc: 0×80070005
Lid: 7343 StoreEc: 0×80070005
Lid: 8047 StoreEc: 0×80070005
Lid: 7310 StoreEc: 0×80070005
Lid: 1750 —- Remote Context End —-
Lid: 31418 — ROP Parse Done —
Lid: 22417
Lid: 30609 StoreEc: 0×80070005
Lid: 29073
Lid: 20369 StoreEc: 0×80070005

Exchange Management Shell command attempted:
New-PublicFolder -Name ‘test’ -Path ‘\’ -Server ‘Server Name’

Elapsed Time: 00:00:00

Open the Adsiedit.msc tool.

Expand the CN=Configuration container, and then locate the following container: CN=Services, CN=Microsoft Exchange, CN=[Org_name], CN=Administrative Groups, CN=First Administrativeroup, CN=Folder Hierarchies, CN=Public Folders
Right-click CN=Public Folders, and then click Properties.

On the Security tab, from the Users and Groups list, click the Everyone group.
Clear the Deny check box for the Create named property in the information store property.