When i am trying to use site content and structure move from one document library to another i get error . It states Attempt to move fail and 

<error><customData>d6b2cf5f-c9ab-4769-b36e-b7408321f1a8: Only farm admin can enable or disable throttling.</customData></error>

What can be done by farm side to make this work? 

Hi

You might have list items more than expected.You have to disable throttling for that list or library.

$Site  =  Get-SPWeb -Identity <SiteURL>
$List  =  $Site.Lists[List Name]
$List.EnableThrottling =  $false

$List.Update()

Source document library just has 4 documents and destination has just 2. It is well below LVT so why would i need to disable throttling?

This would work but, and it's a big but, make sure you turn it back on after you run the migration. It's fine for a short while but it isn't something you want to leave turned off unless you really have to do so.

Just to move document from a library with 4 docs to library with 2 docs, i have to turn off the throttling. Is it even correct? Is this how site content and structure move was designed to work?

Nope, if you've only got 4 columns then you're getting that message for another reason. I'm not sure what that might be, how many columns of each type does that library have?

The source document library has checked out to column but destination does not. That is the only difference. 

I was getting this error as well. I had a web part on the site page that had a custom view. That custom view was messing things up. I deleted the web part and it was fine.