I'm trying to work this out and I'm still getting confused
Say i have the product of transpositions
$\tau = (1 6)(3 2)(1 5)(1 4)$
How does 1 map to 6? The way i'm reading it is that 1 maps to 4 and since 4 isn't contained anywhere else in the other cycle's 1 maps to 4 overall.
This is wrong, I need a detailed explanation on how to read products of transpositions.