The easiest way to solder multi pin connector?

https://www.parts-express.com/Desoldering-Pump-370-030

Heat, de-solder and suck the old solder off.

I use a sharp round pick after I pull the solder off. I insert it and make sure the hole is de-burred. Clean the pins or wires with a little isopropyl, insert them through the cleaned up holes and little dab of flux and solder. Clean afterwards with isopropyl alcohol. Check your work. If there is any issues, repeat the process. 

It will take longer to heat up the soldering iron than to do the work. :-)

Regards

De-solder braid is just fine. Clean like Dave said. 

Most important with boards like this is to use the right temp and right size solder tip and even then be especially careful not to overheat. Because your biggest risk on a PC board is overheat and lift or burn the trace. Especially with a lot of them close together like this. 

First, learn to solder. I bet there are some videos on YouTube. Then get the right equipment and practice until you get the hang of it. 

@russ69 ,

I’d second that. There’s nothing like practice when it comes to soldering.

Cleanliness is crucial. Otherwise the solder doesn’t stick well.

I used isopropyl alcohol when replacing the 3.5mm jack on my Sennheiser headphones.

Here's the first one of a nice video series on YouTube I found both helpful and informative.

A temp controlled device is essential for these larger items.

I use a combination of pumps and solder wick. 

Get into the habit of using needle nose pliers to move those headers, not your bare hands. :D

If you want to do this right, then get the desoldering gun in the link below. Trying to use a manual solder sucker or braid can be difficult and leads to mishaps.  This desoldering gun makes easy work of it. If you plan to desolder more in the future, then it is a must have purchase. First use your soldering iron to reflow the solder pads you plan to use the gun on. 

OMG, if you don't know how to solder, find a friend that does or just buy a pre-made cable even if it has more wires than you need. 

Thank you everyone, I am able to desolder with the help of my father. He was repairing cathode tube TV as a part time job when he was young. 

What we used to desolder was Weller gun and solder sucker as some members here suggested. 

This is a 1 time project so I didn't opt to buy the desoldering machine, which is obviously the best solution. 

Thank you everyone for your input!