I SOLD MY HOME AND GIFTED THE EQUITY TO MY CHILD. HOW DOES THE GIFT OF EQUITY APPLY? IS IT A DEDUCTION OR AN EXPENSE?

[MinhT1]

Gifts are not deductible for the donor and not taxable for the recipient.

The donor has to file a Gift tax return (form 709 - not supported by TurboTax) if the gift to a recipient is more than the annual exclusion of $15,000 (2022: $16,000).

[Bsch4477]

As I understand your post you sold your home to someone and then gifted the proceeds to your child. If that is correct you complete a gift tax form 709 in the amount of those proceeds and mail it to the IRS. 

A gift of equity means that you sold your home to the child at a price below market value. The amount of the gift is then the difference between the sales amount and the market value.