It's a riddle from The Big Little Book of Irish Wit and Wisdom and references a person milking a cow.
a rank bank
The hink-pink for 'when you run to the bank to quickly get some holiday shopping money, you make a' is 'Cash-Dash'.
four door
cash dash
dragon wagon
A four-syllable hink pink is called a "hinky pinky." This type of wordplay involves creating rhyming word pairs where each word has two syllables.
Lunch punch! :) These hink pinks are HARD!
Fake bake is a Hink-Pink for counterfeit cook.
The Hink Pink for a holiday donkey is a Yule mule.
Thin inn is the hink pink for skinny hotel.
The hink pink for "boy's test" is "lad's quiz."
Hink-pinks are usually adjective-noun combinations. That question is usually "What is a hink-pink for an artificial body of water?" The answer is a "fake lake."