how do I graph these?

i have 2...

1) |x-y|+|x+y|+|x|+|y|=12

I tried graphing this but did not end up with the graph depicted in the answers....could anyone help me out with how to solve/graph this?

2) 1/|x+2|

What I did:

x can't equal -2, y can't equal 0

x > -2; y=1/x+2 ( i graphed this line)

x<-2; y=1/-x-2 (i graphed this but it fell below the x-axis)

the second graph (1/-x-2) is supposed to be flipped up

I understand why (its absolute value so everything is positive) but when i graph it it doesn't end up that way....

how to i solve/graph it properly? is there something wrong with my method?

thanks!!