hi, i did D1 with edexcel but i assume it's the same.
firstly you select the odd order vertices, as you have done, then you work out the distances of all the possibilities of repeating them, so repeating either
AD and KH, AH and KD or AK and HD.
AD and KH would be 27(ABD) +30(KJH) =57
AH and KD would be 20(ACH) + 20(KID)=40
AK and HD would be 46(ABEIK) + 40(DIFJH) =86
you repeat AH and KD because it is shortest and then add that to the weight of the network, so 308 + 40 = 348minutes
hope that helped.