A word has been written in four different ways, out of which only one is…

Concept

For a "choose the correctly spelt word" item, the standard method is to recall the dictionary-correct spelling of the intended word letter-by-letter, then check each candidate option against that reference form — paying close attention to any letter that is doubled, or wrongly doubled/undoubled, since that is exactly where spellers commonly slip.

Application

The word being tested here is, per standard English dictionaries (e.g. Merriam-Webster, Oxford), spelled p-a-r-a-l-l-e-l — a single 'r' and a doubled 'l' between the two vowels, eight letters in total. Checking each of the four written forms against this reference:

• Parralel — the 'r' is doubled ('rr'); the 'l' is not doubled. Eight letters in total.

• Paralel — neither the 'r' nor the 'l' is doubled. Seven letters in total.

• Parralell — both the 'r' ('rr') and the 'l' ('ll') are doubled. Nine letters in total.

• Parallel — the 'r' is not doubled; the 'l' is doubled ('ll'). Eight letters in total.

Cross-check

Comparing against the reference form p-a-r-a-l-l-e-l (single r, doubled l, eight letters): only "Parallel" matches on every count — the other three forms either double the wrong letter, fail to double the 'l', or drop a letter altogether.

Therefore, the correctly spelt word is Parallel.