Four sentences are given below as A, B, C and D. Choose the sentence that is grammatically incorrect in describing the use of state issued currencies in early dark web transactions.

Introduction / Context:
This question evaluates your ability to choose the grammatically correct sentence in a modern technological context involving dark web transactions. It focuses on correct preposition choice, natural word combinations, and the way we talk about using currencies to carry out transactions in formal English.

Given Data / Assumptions:
All four sentences mention dark web transactions and state issued currencies.
The time frame is the early phase of dark web activity when legal currencies were used.
You must identify the grammatically incorrect option.
Assume the context is a formal article or passage about digital crime and online markets.
The core idea is that legal state currencies were used to carry out transactions on the dark web.

Concept / Approach:
The standard collocation in English is to carry out transactions or to use a currency to carry out transactions. Prepositions like in, on and between must be used logically with nouns such as transactions or web. Also, dark web is normally treated as a singular space, not as dark webs. The strategy is to eliminate sentences that misuse prepositions or create unnatural phrases such as carry in the transactions between the dark webs.

Step-by-Step Solution:
Step 1: Check option A. Dark web transactions were initially carried out using legal state issued currencies is grammatically sound. The phrase carried out using is a correct collocation. Step 2: Check option B. In the early days, dark web transactions were carried out using legal state issued currencies is also correct, with clear time reference in the early days. Step 3: Check option C. Legal state issued currencies were used initially to carry out transactions on the dark web is again grammatically correct and uses the idiomatic phrase to carry out transactions. Step 4: Check option D. The legal state issued currencies were used to initially carry in the transactions between the dark webs is problematic. Step 5: The phrase carry in the transactions is incorrect, because the standard pattern is carry out transactions. In addition, between the dark webs is illogical, since there is normally one dark web, and between requires two or more distinct things. Step 6: Therefore, option D is the only sentence that is grammatically and collocationally incorrect.

Verification / Alternative check:
Try simplifying option D. If you write currencies were used to carry in transactions, it still sounds wrong. Replacing carry in with carry out immediately improves it, confirming that the preposition in is not acceptable here. Similarly, changing between the dark webs to on the dark web would fix the latter part, reinforcing that the original phrase is flawed.

Why Other Options Are Wrong:
Option A is acceptable because carried out using legal state issued currencies is a standard way to describe how transactions were executed.
Option B is acceptable because the sentence structure and word order are normal and clearly express time and action.
Option C is acceptable because used initially to carry out transactions on the dark web follows standard collocations for finance and online activity.
Option D alone misuses carry in and between the dark webs, so it is the incorrect choice.

Common Pitfalls:
A frequent mistake is to ignore small words like prepositions in long sentences. However, in phrasal verbs and fixed expressions, changing a preposition can completely break the grammar. Another pitfall is to accept unusual phrases simply because the topic, such as dark web, feels unfamiliar, but examinations expect standard English regardless of subject matter.

Final Answer:
The grammatically incorrect sentence is Option D. The legal state issued currencies were used to initially carry in the transactions between the dark webs.