Guys have mathematical rules on the ages of socially acceptable sexual partners (half your age plus seven is a good one).
To do fuck maths is to mathematically work out whether somebody falls within the age limits.
I'm 20 she's 16, which is not quite half my age plus seven. But I did the fuck maths and in 2 years I'll be 22 she'll be 18 which will make it OK.
To initiate a hug by, quite literally, showing your palms while your arms are out by your sides.
I didn't think we were all that close but at the end of the night she showed palms so I hugged her goodbye.