This is from a Youtube video on the Chinese Remainder Theorem -https://www.youtube.com/watch?v=ru7mWZJlRQg
The value at each column is the product of the mod of the two other columns(so moding will reduce to one value)
The author is currently on the step to ensure x, which is composed of a sum of congruences, is
$\equiv$ 2(mod 4). Once he applied modulus 4 to all the congruences, he was left with x $\equiv$ 3(mod 4) which isn't the same as x $\equiv$ 2(mod 4). To do this the author recommended taking an approach of converting 3 (mod 4) to 1(mod 4) then to 2 (mod 4). Why doesn't the author go straight from 3 mod 4 to 2 mod 4 by multiplying the 15 by 2? That way x $\equiv$ 6 $\equiv$ 2 mod(4). Is there a reason he chose this roundabout approach and not the direct approach?