Arrange the given words in the sequence in which they occur in the dictionary.
i. Beguile
ii. Bigot
iii. Begun
iv. Bigamy

To arrange the words in alphabetical/dictionary order, we compare them letter-by-letter:
All words start with 'B'.

Compare the second letters:

'e' comes before 'i'. So, Beguile and Begun come before Bigot and Bigamy.

Compare Beguile (i) and Begun (iii):

First four letters are identical ('Begu').

The 5th letter of Beguile is 'i' and for Begun is 'n'. Since 'i' comes before 'n', Beguile (i) comes first, followed by Begun (iii).

Compare Bigamy (iv) and Bigot (ii):

First three letters are identical ('Big').

The 4th letter of Bigamy is 'a' and for Bigot is 'o'. Since 'a' comes before 'o', Bigamy (iv) comes before Bigot (ii).

Combining the entries gives the sequence: i, iii, iv, ii.