How Do I run Powershell x86 from Powershell?

Start-Process $Env:WINDIR\SysWOW64\WindowsPowerShell\v1.0\powershell.exe

I recommend Caleb's answer. But personally, I have a function in the PowerShell profile that loads on startup and launches a new PowerShell x86 shell when running x86 as this is so commonly required.

Function x86{
    Start-Process $($env:SystemRoot + "\syswow64\WindowsPowerShell\v1.0\powershell.exe")
}

_{NB: $env:windir and $env:SystemRoot are equivalent here. Maybe not always}

You will need the complete path to the x86 Powershell executable. If you are launching it from the command prompt (CMD.EXE), you would use

start "" "%SystemRoot%\SysWOW64\WindowsPowerShell\v1.0\powershell.exe"

If you were starting it from a PowerShell session, you would use

start "" "$env:SystemRoot\SysWOW64\WindowsPowerShell\v1.0\powershell.exe"

or

Start-Process -FilePath "$env:SystemRoot\SysWOW64\WindowsPowerShell\v1.0\powershell.exe"