Solitaire game where you deal four up, four down
The game you are looking for is a mixture between the classic solitaire games Scorpion  and Yukon.

I've looked through over 700 games in both SolSuite Solitaire and Pretty Good Solitaire and I came really close to finding your game in a variation called Geoffrey (by Thomas Warfield) in Goodsol's game Pretty Good Solitaire. The only difference is that Geoffrey is played with the last 2 cards dealt face up (instead of just the last card) in the last 4 columns.



Geoffrey
https://www.goodsol.com/games/geoffrey.html 

Info
 - 1 Deck.
 - Success rate - Medium (30%).
 - Mostly Skill.  

Layout
 - 4 Foundation columns (on top) - Build up in suit from Ace to King.
 - 8 Tableau columns (below foundation) - Build down in suit.
 - No Stock  

Object of the game
To create four suites of 13 cards each in an ascending suit sequence from Ace to King, by moving all the cards from the tableau to the foundation.  

Tableau
 - 52 cards in eight columns.
 - At the start of the game 7 cards are dealt to the first 4 columns and 6 cards are dealt to the next 4 columns.
 - In the first 4 columns, all cards are dealt face up. In the next 4 columns the first 4 cards are dealt face down and last 2 cards are dealt face up.

Rules
 - Tableau columns must be built down in suit, e.g. a 10 of ♠ can only be played on a Jack of ♠.
 - Any face up card, no matter how deep it is in a column, may be moved to make a build. All covering cards are moved with it together as a unit.
 - When a face down card is uncovered, it is automatically turned face up and is available for play.
 - Nothing can be placed on an Ace. A King cannot move, except to an empty space.
 - Spaces can only be filled with a King or groups of cards headed by a King.
 - Foundation columns must be built up in suit from Ace to King.
 - The top card of each tableau column is available for play to the foundations.
 - The game is won if the entire deck in all four suites has been moved to the foundation.  

Here are some other examples of similar games:

Scorpion from SolSuite Solitaire 


ScorpionCell from SolSuite Solitaire


Scorpion
https://www.politaire.com/scorpion

Applegate
https://www.politaire.com/applegate

Scorpion Head
https://www.politaire.com/scorpionhead

Three Blind Mice
https://www.politaire.com/threeblindmice

Farmers Wife
https://www.politaire.com/farmerswife

Double Scorpion
https://www.politaire.com/doublescorpion

Russian Solitaire
https://www.politaire.com/russian