Seeing your method 1 answer, it seems like you forgot that 42 dollars is for 6 guests, not just 1. The unit rate is the rate per guest, and if we divide 42 by 6, we get 7dollars/1person as our unit rate. Since 7 dollars is our unit rate, we can multiply that by 72 to get 504 dollars, therefore making 500$ per night more cost effective.
Another way to do this is to do 42*72, as you did, but then dividing the final product by 6 due to that 42*72 is for 72*6=432 guests (we get the 6 since the unit rate is 7$ per person and 42/7=6). Doing that, we get 3024/6=504, which is still greater than 500