for federal tax purposes, the 'cost basis' is whatever your parents paid for the home plus improvements made along the way. That compared to the net sales proceeds is the taxable income (divided by 3). It only gets taxed at capital gains rates since you owned it for more than a year.
The fact that it was worth $160k and it was sold for $120k is immaterial to the situation
see the link below and especially the section under 'gifts'
If you sell for a profit, your basis is the same as the basis of the previous owner.
https://turbotax.intuit.com/tax-tips/rental-property/cost-basis-tracking-your-tax-basis/L4i1f9qB1
