Step 1: Understand the task.
We must arrange four words in correct dictionary order. The words are (i) Sycamore, (ii) Syllable, (iii) Sycophant, (iv) Syllabus.
Step 2: Compare letter by letter.
All four start with 'Sy'. The third letter splits them. 'Sycamore' and 'Sycophant' have 'c', while 'Syllable' and 'Syllabus' have 'l'.
Step 3: Decide which group comes first.
In the alphabet 'c' comes before 'l'. So the two 'Syc' words come before the two 'Syl' words.
Step 4: Order the 'Syc' group.
Compare 'Sycamore' and 'Sycophant' at the fourth letter. 'a' in 'Syca' comes before 'o' in 'Syco'. So 'Sycamore' (i) comes before 'Sycophant' (iii).
Step 5: Order the 'Syl' group.
Compare 'Syllable' and 'Syllabus' further along. They match up to 'Syllab', then 'l' in 'Syllable' comes before 'u' in 'Syllabus'. So 'Syllable' (ii) comes before 'Syllabus' (iv). The full order is (i), (iii), (ii), (iv).
Step 6: State the conclusion.
The correct alphabetical order is (i), (iii), (ii), (iv).
\[ \boxed{(i),\ (iii),\ (ii),\ (iv)} \]