Theory:

Syllabification refers to the process of division of words into smaller parts, known as syllables - based on the sounds they produce. The method involves splitting of words into units of sounds or sounds of vowels. A syllable is a unit of pronunciation having one vowel sound.
Example:
1. Run - "U" is the vowel that produces a syllable. Therefore, the word had one syllable.
2. Acting - Act-ing: "A" and "I" are the vowels that produces two different sounds. Therefore there are two syllables in this word.
3. Australia - Au-stra-lia: has "Au" producing a sound, "stra" producing a sound, "Lia" producing a sound; therefore, there are three syllables in this word.
Important!
In simple words, syllabifying is the process of dividing the words according to the vowel sounds.
There are six types of syllabification:
 
Syllabification.JPG
 
Note: The most common types are monosyllabic, disyllabic and polysyllabic words.
 
Let us syllabify a few words to understand the syllabification process better:
Process of syllabification:
  
1. Read the word
2. Identify the vowels.
3. Break the words according to the vowel sounds.
Some words from the lesson "Adventures of Don Quixote":  
 
No.
Word
Split into
No. of syllables
Syllabification type
1AdventureAd-ven-ture
\(3\)
Trisyllabic
2CourageousCou-ra-geous
\(3\)
Trisyllabic
3IncredibleIn-cred-i-ble
\(4\)
Terasyllabic
4KnightKnight
\(2\)
Monosyllabic 
5HilariousHi-lar-i-ous
\(4\)
Terasyllabic
6ExcitementEx-cite-ment
\(3\)
Trisyllabic
7PeasantPeas-ant
\(2\)
Disyllabic
8ImagineIm-ag-ine
\(3\)
Trisyllabic
9EntreatEn-treat
\(2\)
Disyllabic
10ShepherdShep-herd
\(2\)
Disyllabic
11HappilyHap-pi-ly
\(3\)
Trisyllabic
12CarefullyCare-ful-ly
\(4\)
Terasyllabic
13EnoughE-nough
\(2\)
Disyllabic
14EstateEs-tate
\(2\)
Disyllabic
15DefeatDe-feat
\(2\)
Disyllabic
16GiantGi-ant
\(2\)
Disyllabic
17PrincipalPrin-ci-pal
\(3\)
Trisyllabic
18LeaderLead-er
\(2\)
Disyllabic
19HonourHon-our
\(2\)
Disyllabic
20RecklessReck-less
\(2\)
Disyllabic
21AbsolutelyAb-so-lute-ly
\(4\)
Terasyllabic