Answer:
AB+BE+EF+GF+HG+AH = 14 #EQU 1
BC+CD+DE+EF+GF+BG = 22 #EQU 2
AB+BC+CD+DE+EF+GF+HG+AH = 24 #EQU 3
IMPLEMENTING EQU 2 IN EQU 3
AB+22-EF+ HG+AH = 24 # EQU 5
FROM EQU 1
AB+HG+AH = 14-(BE+EF+GF) #EQU 4
IMPLEMENTING EQU 4 IN EQU 5
22+14 - (BE+EF+GF+EF) = 24
36 - 24 = BE+EF+GF+BG(EF=BG)
12 = PATH TAKEN ON THURSDAY