The question raised
From the Saddharma-Puṇḍarīka, or Lotus of the True Law, translated from Sanskrit by H. Kern, Sacred Books of the East, vol. XXI (Oxford: Clarendon Press, 1884) — public domain. Chapter XXIV (= Kumārajīva ch. 25), 'Samantamukha-parivarta,' the Universal Gate of Avalokiteśvara — the chapter chanted in Sōtō and Rinzai halls as the Kannon-gyō.
At that moment the Bodhisattva Akshayamati rose from his seat, put his upper robe upon one shoulder, stretched his joined hands towards the Lord, and said: 'For what reason, O Lord, is the Bodhisattva Avalokiteshvara called Avalokiteshvara?' On this question the Lord answered the Bodhisattva Akshayamati:
'All the hundred thousands of myriads of creatures, young man of good family, who in this world are suffering troubles will, if they hear the name of the Bodhisattva Avalokiteshvara, be released from that mass of troubles. Those who shall keep the name of this Bodhisattva, young man of good family, will, if they fall into a great mass of fire, be delivered therefrom by virtue of the lustre of that Bodhisattva.'
Liberation from peril
'If they should be carried off by the current of rivers as great as the Ganges, they will, by appealing to Avalokiteshvara, find a ford. If many hundred thousands of myriads of beings, gone to sea in a ship for the sake of treasure, are tossed by a black gale, they have but to invoke Avalokiteshvara and they shall all be saved out of that fearful gulf.'
'If a man given up to capital punishment implores Avalokiteshvara, the swords of the executioners shall snap asunder. Were the universe filled with goblins and giants, they would, by virtue of the name of Avalokiteshvara being pronounced, lose the power of sight in their wicked designs.'
The thirty-two forms
'In whatever form a creature is to be saved, in that form does the Bodhisattva Avalokiteshvara reveal himself: to one whom he can save by the form of a Buddha he shows the form of a Buddha; to one whom he can save by the form of a Bodhisattva he shows that form; to one whom he can save in the form of a śrāvaka, a brāhmaṇa, a householder, a layman, a child, a woman, a youth — in any one of these forms — he reveals himself accordingly. Thus inconceivable, young man of good family, are the qualities of Avalokiteshvara.'
The verse
Thereupon the Bodhisattva Akshayamati spoke this stanza:
Avalokiteshvara, with eyes endowed with mercy,
With a glance pure, kind, of love and pity,
Of his own will, like a benefactor of the world,
Saves us from suffering and pain.
The voice of Avalokiteshvara is like the voice of Brahmā,
Like the voice of clouds, like the voice of Mahābrahmā;
It is the voice of perfection, the voice that should be heard,
The voice that fills the hearer with joy.
When this section had been delivered, eighty-four thousand living beings felt their minds filled with delight at the prospect of supreme and perfect enlightenment.