In plain words
Endowed with that faith, the devotee engages in the worship of that form and obtains from it the desired objects, since those results are in truth granted by Me alone.
Word for word
He, endowed with that faith, engages in the worship of that [form], and obtains from it the desired things, those being ordained by Me alone.
The commentators
Bhagavadgītābhāṣyam
ययैव पूर्वं प्रवृत्तः स्वभावतो यः यां देवतातनुं श्रद्धया अर्चितुम् इच्छति —
स तया मद्विहितया श्रद्धया युक्तः सन् तस्याः देवतातन्वाः राधनम् आराधनम् ईहते चेष्टते । लभते च ततः तस्याः आराधितायाः देवतातन्वाः कामान् ईप्सितान् मयैव परमेश्वरेण सर्वज्ञेन कर्मफलविभागज्ञतया विहितान् निर्मितान् तान् , हि यस्मात् ते भगवता विहिताः कामाः तस्मात् तान् अवश्यं लभते इत्यर्थः । ‘हितान्’ इति पदच्छेदे हितत्वं कामानामुपचरितं कल्प्यम् ; न हि कामा हिताः कस्यचित् ॥ २२ ॥
In plain words
With that very faith he already set out with, moved by his own nature — whoever wants to worship, in faith, whatever form of a deity he chooses —
Equipped with that faith — which, remember, I myself set in motion — he pursues the worship of that deity's particular form. And from that worship, he does get what he wanted: the very things he longed for. But make no mistake about who actually grants them — it is I, the Supreme Lord, who alone knows exactly how the fruits of action are to be divided, who ordains and fashions those gifts. Since it is the Lord who ordains them, he is bound to receive them. Some read this differently, as 'beneficial' rather than 'ordained' — but even then, that word can only be understood loosely, as a manner of speaking. Because desires, in truth, are never really beneficial for anyone.
Close to the Sanskrit
By that very [faith] with which he formerly set out, by his own nature — whoever wishes to worship with faith whichever form of a deity —
He, endowed with that faith ordained by me, being so, strives after, endeavors toward, the propitiation, the worship, of the embodied form of that deity. And from that, of that deity worshipped, of the embodied form, he obtains the desires, the wished-for things, ordained, fashioned, by me alone, the Supreme Lord, the omniscient one, by virtue of knowing the apportionment of the fruit of action; for, because those desires are ordained by the Blessed Lord, therefore he necessarily obtains them; that is the meaning. [Reading it as] 'hitān' in this alternative word-division, the quality of being beneficial must be figuratively construed of desires; for desires are not truly beneficial for anyone.