The correct option is
B P-R-S-Q
The normal sequence of a sentence in active voice is: Subject followed by verb. The subject of a sentence should be a noun which performs the action. In the given phrase, the nouns are in part Q (house) and part R (boy). The verb (walked) follows the noun, 'boy' in phrase R. Hence, the boy must be the subject.
The article 'a' precedes a word which begins with a consonant sound. Hence, the word, 'a' should precede 'boy'.
The article, 'an' precedes a word which begins with a vowel sound. Hence, the word, 'an' should precede the word, 'empty'.
Given the above, the correct sequence is: 'A (P) boy walked (R) into an (S) empty house (Q)'. This is grammatically correct and makes a meaningful sentence. Hence, option B is correct.
Option A is incorrect as the word, 'empty' (which begins with a vowel sound) cannot be preceded by the article 'a'.
Option C: The article 'a' is a determiner and should be followed by nouns or noun equivalents. It cannot be followed by a preposition (into). Hence, this option is incorrect.
Option D: The article 'an' cannot precede the word, 'boy' (which begins with a consonant sound. Hence, R cannot follow P and option D is incorrect.