I bought home with brother in 2010 for 212k. In 2018 he did a cash refi increasing loan to 300k and got the cash. I sold for 465k. How do I show I only got 165k?

what was the home used for - yourselves or was it a rental?

when you say you sold for $465, I assume that was the full sales price not your share

assuming the original purchase was a 50/50 deal your starting basis is $106K

assuming half ownership your share of the sales price was $232.5K and with no rental, your gain would be the difference further reduced by selling costs 

you need to work out the mortgage issue with your brother. this is not a tax issue since the mortgage balance does not figure into your basis or his and thus the gain.

Taking out money doesn’t change the basis, it just changes when you receive the profit from the sale. 

If you and your brother sold a home together, that each of your bases is $106,000, and each of your sales proceeds is $233,000, resulting in a capital gain to each of you of $127,000.  If that seems unfair because your brother took out a refinance a while ago, that is something you have to address with your brother.

If you are the sole owner now, how did you obtain sole possession? If it was a buyout or an inheritance, either of those situations might have adjusted your basis. But you still can’t take full account of the money that was previously withdrawn.