Horror is related to Surprise. Surprise is related to Birthday. Birthday is related to Year. Year is related to Old. 
Hard is related to Shoe. Shoe is the opposite of Hat. 
Horror <--RelatedTo--> Surprise <--RelatedTo--> Birthday <--RelatedTo--> Year <--RelatedTo--> Old 
Hard <--RelatedTo--> Shoe <--Antonym--> Hat 