Interesting video. Expensive product. I should think a copy of Combination Challenge (the red book) would stand you in good stead. It seems like this Visualwize is a similar tactical trainer; and the red book is known to help improve chess visualization/tactics. It's also pretty expensive, but a used copy will be cheaper surely.
Can't link the book, sorry :/ But I found 4 used copies online for ~USD21. Not too shabby!
The key to beginning to calculate more accurately is to recognize patterns; the way to begin developing your memory bank of those patterns efficiently is to practice a sample set of tactics (not random puzzles) over and over, until you can solve every problem in that set rapidly.
This is called "The Woodpecker Method" of doing things, and Axel Smith and Hans Tikkanen developed it the method back in 2010, which allowed Tikkanen to achieve his three GM norms in a seven-week period.
The book is now on Chessable, and I highly recommend it; the work really helped me, and Chessable's spaced-repetition format complements the book well. I think it's around $30, but you get unlimited access to it and can use it on Chessable to train.
Looking 8 moves ahead is completely arbitrary, and entirely depends on the complexity of the position. Some positions I can see 10 or more moves ahead when it's the endgame and there are few reasonable choices.
On the other hand sometimes a lot of material is on the board an even seeing 2-3 moves ahead is difficult.
Well I guess the books "promise" is that you can visualize the situation and examine it 8 moves from now. Problem remains how to pick variations. 8 moves deep calculation is usually impossible. Only in forcing situations