Step 1: The International Day of Yoga is celebrated annually on 21st June.
Step 2: The idea was proposed by the Prime Minister of India, Narendra Modi, during his speech at the United Nations General Assembly in 2014.
Step 3: The date 21st June was chosen because it is the summer solstice in the Northern Hemisphere — the longest day of the year — which holds special significance in many cultures.
Step 4: The first International Day of Yoga was celebrated worldwide on 21st June 2015, with millions participating in mass yoga sessions.
Step 5: Other options:
- 18th April has no link to Yoga.
- 31st May is observed as World No-Tobacco Day.
- 5th June is observed as World Environment Day.
Thus, the correct answer is $\mathbf21st\ June$.