Located at the very coal mines that provided them with fuel, the use

(so I typed out the sentence just because I want to do a proper take on it.)

Located at the very coal mines that provided them with fuel, the use of steam engines in eighteenth-century England increased coal production by allowing for mines to be drained of water and permitting extraction of deeper layers of coal.

a) the use of steam engines in eighteenth-century England increased coal production by allowing for mines to be drained of water and permitting.
b) steam engines increased goal production in eighteenth-century England by permitting the drainage of mines and the
c) steam engines in eighteenth-century England allowed an increase in coal production by permitting the drainage of mine water and permitting
d) steam engines increased cold production in eighteenth-century England by allowing water to be drained out of mines and
e) eighteenth-century use of steam engines increased English coal production by draining mines and

From reading the first words of the sentence I immediately notice that it's a modifier and every time there is a modifier my brain goes off screaming 'MAKE SURE IT'S MODIFYING THE RIGHT SUBJECT!'. So since from the start we can identify several issues:
1. Modifier issue 'the use of the steam engine' - I am pretty sure the use is not located, instead the first half of the sentence should modify 'the steam engine'
2. Parallelism issue with 'allowing for mines TO BE DRAINED[...] and permitting EXTRACTION[...]'; first is a gerund + passive and second is gerund + noun phrase.

With these analysis in mind, I quickly eliminate A and E. We're left with B, C, and D.

B) looks good so far, it fixes the modifier issue and the parallelism issue so I move on to scan the remaining choices.

C) this answer choice changes the meaning of the original intention whereby it talks about how steam engines helped coal production in the 18th century and not 18th century steam engines helping coal production. Therefore I eliminate this answer choice. Additionally, two permitting sounds awkward and redundant.

D) Fixes the modifier issue but the parallelism issue still remains, therefore I eliminate this choice.

B) is the only one we have left and corrects all the errors