To find the Active Directory (AD) groups that a user is a member of, you can use the Get-ADPrincipalGroupMembership cmdlet in PowerShell.

# Import the ActiveDirectory module  
Import-Module ActiveDirectory  

# Get the AD user object  
$User = Get-ADUser -Identity John Smith  

# Get the AD groups that the user is a member of  
Get-ADPrincipalGroupMembership -Identity $User

The Get-ADPrincipalGroupMembership cmdlet returns an array of ADGroup objects representing the AD groups that the user is a member of. You can use the Name property of each ADGroup object to get the name of the group.

You can also use the -Recursive parameter to get the nested membership of the user, which includes the groups that the user is a member of, as well as the groups that those groups are a member of, and so on.

You can find more information about the Get-ADPrincipalGroupMembership cmdlet in the PowerShell documentation.