Shrila Rupa Goswami's Laghu Bhagavatamrta Text 78:
nandanabhyam ca samyutah
kausalyayam – in the womb of Kausalya-devi; dasarathat – from Dasaratha Maharaja; nava – fresh; durva-dala – durva grass; dyutih – with the splendor; tretayam – during the Treta-yuga; avirabhavat – appeared; caturvimse – during the 24th; catuh-yuge – cycle of four yugas; bharatena – by Bharata; sumitrayah – of Sumitra; nandanabhyam – by the two sons (Laksmana and Satrughna); ca – also; samyutah – accompanied.
"Splendid as a new blade of durva grass, and accompanied by Sumitra's two sons and by Bharata, Lord Ramachandra appeared in the Treta-yuga of the 24th catur-yuga as the son of Kausalya and Dasaratha."
It is clearly mentioned that caturvimse catur yuge i.e. during the 24th caturyuga.
1 Catur-yuga = 4,320,000 years or 43 lakh 20 thousand years.
Catur-yugas passed = 24th part (roughly half) of Treta & full Kali, 25th, 26th, 27th, 28th till part of Kali-yuga.
Years passed approx. = 432,000 + 432,000 + 4,320,000 + 4,320,000 + 4,320,000 + (4,320,000-427,000 left)
= 17,717,000 (+ or – 432,000 years)
(+ or – 432,000 years is required because we don't exactly know in which period of Treta Yuga of the 24th Chatur-yuga Lord Rama appeared).
This is a most beautiful & detailed narration about the appearance of Lord Ramachandra from the book (Valmiki) "Ramayana" by Shriman Purnaprajna dasa.