I'll assume that this is a distribution from a traditional 401(k) account and there is no after-tax basis involved. There would have been a mandatory 20% withheld for taxes, so you effectively had constructive receipt in 2017 of at least this portion of the distribution. However, with the check for the other 80% mailed to the wrong address and you not receiving the check until late April 2018, you could not have had constructive receipt until late April. If it's your desire to treat this as taxable income for 2017, simply enter the Form 1099-R as received into 2017 TurboTax as DoninGA described. However, you can potentially make the argument that, because you did not have constructive receipt of the 80% until 2018, this portion can be treated as 2018 income instead and would be reportable on your 2018 tax return. However, doing so would likely involve filing substitute Forms 1099-R (Forms 4852), one for 2017 and another for 2018 to substantiate this reporting, so this would raise the scrutiny by the IRS. If there is no significant advantage to delaying this income to 2018 (the likely case given that the amount is small), there is no reason to complicate your reporting. No matter what you do with the 80%, the 20% withholding needs to be reported on your 2017 tax return.
Did you roll this distribution to another retirement account? Even if you have not already rolled it over, you should still be able to roll the 80% over, either based on a constructive receipt date of late April 2018 and therefore still within the 60-day rollover window, or under self-certification that the circumstances would qualify for a waiver of the 60-day deadline. If you roll the 80% over, you would simply report the entire distribution on your 2017 tax return and indicate the amount rolled over. (Given that you had in 2017 constructive receipt of the 20% withheld for taxes, I see no justification for being able to now roll over that portion, beyond 60 days after December 27, 2017.) Any portion rolled over would avoid the 10% early-distribution penalty on that portion.
