'the' is a definite article, as such it modifies nouns and noun phrases (NP). In this case the noun phrase (NP) is 'the price' which is made up of, the = definite article or a determiner, and price = noun. And 'twice' traditionally considered as an adverb but the current linguistic knowledge renamed it as a "predeterminer" in other words it comes before a central determiner (the) and modifies the whole noun phrase. That is the way it is in English, basically these are the kernel structures of English syntax, ergo, questions, such as "Why is this like that" may not be answered logically. Languages are not often logical.
If you care further information on this subject, your best bet is to find a copy of A Comprehensive Grammar of the English Language, Quirk et al., and read the Noun Phrases/Determiners.