If, in a certain code language : "black colour Pen" is coded as : 356 "white…

Concept: In sentence-based coding (also called "Chinese coding"), a whole phrase is coded by a group of numerals given in no fixed order, so no numeral can be attached to a word by its position. The mapping is recovered only by comparison across phrases: a numeral common to two coded phrases must stand for a word common to those phrases, and once a word’s numeral is fixed it can be removed from every phrase that contains that word. Repeating this elimination isolates the words one at a time.

Application: Compare the three coded phrases pair by pair.

1. "black colour Pen" → 356 and "white colour flower" → 587 have exactly one word in common, colour, and exactly one numeral in common, 5. Therefore colour = 5.

2. "black colour Pen" → 356 and "red colour Pen" → 345 have two words in common, colour and Pen, and two numerals in common, 3 and 5. Since colour = 5 is already fixed, the other shared numeral gives Pen = 3.

3. Remove colour = 5 and Pen = 3 from "black colour Pen" → 356. One word, black, and one numeral, 6, are left. Therefore black = 6.

4. Remove colour = 5 and Pen = 3 from "red colour Pen" → 345. One word, red, and one numeral, 4, are left. Therefore red = 4.

5. The question asks for black first and red second, so the required codes are 6 and 4.

Cross-check: The full mapping recovered from the data, and how each entry was fixed:

Substituting back reproduces every given code: black + colour + Pen = 6, 5, 3 → 356; red + colour + Pen = 4, 5, 3 → 345; white + colour + flower uses 5 together with 8 and 7 → 587. The data is therefore fully consistent. That white and flower stay interchangeable does not matter here, because the question asks only about black and red.