realistically all this or any other process is doing is expansion and taking advantage of the commutative nature of multiplication.
(70 + 9)x(80 + 6)
70x80 + 9x80 + 6x70 + 6x9
56(00) + 72(0) + 42(0) + 54
Guess what - long story short you need to know your times tables. I don't see how the lines method is any easier than long multiplication, which in itself is not hard with a little time and explanation. If you can use the lines, or any other method, as a way of conveying what I did above - then you've succeeded.
Edit: Stars go to italics and I don't know the escape character
> I don't see how the lines method is any easier than long multiplication
You probably learned multiplication using something similar to the lines method. If you had 3 x 4, you'd draw out 3 circles and then put 4 more circles inside and count up all the small ones. This is just a logical extension of that.