taking money from property A to buy property B

Hello,

I just did a cash back refi on property A. Property A is held in an LLC and has an associated biz checking account. The bank put the cash back straight into that account. Now I am needing most of that cash for a down payment on Property B. Property B will soon be held in an LLC, and already has the biz checking account set up. I checked with a lawyer about how to properly move the money. They said take it as distribution to me personally, then move it to the new LLC account as a capital contribution. Makes sense for liability. However they said that distribution to me would be a taxable event. Which means I am going to be taxed on a cash back loan - which doesn't seem right.

It's a pretty common technique to take cash out of one property and use it to buy another.   
So I'm curious to see how others do this transferring around to avoid the tax ding.   If it's even possible.    Thanks!