You lost minus when you were adding two equations.
-176= - 22x -12y
144 = 6x +12y
-32= - 16x
x=2
88=11x+6y,
88=11*2+6y
6y=66
y=11
Check:
88=11x+6y=11*2+6*11=88 True
144=6x+12y=6*2+12*11=12+132=144 True
The cost of daylilies is $2.
The cost of pot of ivy is $11.