Explanation:

Home Rule Movement (1916) was started by B. G. Tilak (1916) at Poona and Annie Besant and S. Subramania Iyer at Adyar, near Madras (Sept, 1916).
Objective: Self government for India in the British Empire. Tilak linked up the question of Swaraj with the demand for the formation of Linguistic States and education in vernacular language. He gave the slogan: Swaraj is my birth right and I will have it.
Lucknow Pact (1916) - Happened following a war between Britain and Turkey leading to anti-British feelings among Muslims. Both INC and Muslim League concluded this (Congress accepted the separate electorates and both jointly demanded for a representative government and dominion status for the country).
August Declaration (1917) - After the Lucknow Pact, a British policy was announced which aimed at increasing association of Indians in every branch of the administration for progressive realization of responsible government in India as an integral part of the British empire. This came to be called the August Declaration.
Khilafat Movement (1920) - Muslims were agitated by the treatment done with Turkey by the British in the treaty that followed the First World War. Two brothers, Mohd. Ali and Shaukat Ali started this movement.