Syllabification is a highly controversial topic in phonology. There are many different approaches to syllabification and most of them sound nonsensical, but I'll give it a shot.
Bear in mind that syllables are a unit of 'spoken language' and have nothing to do with spelling.
The Oxford English Dictionary defines a syllable as 'A vocal sound or set of sounds uttered with a single effort of articulation...'.
The technical part of the definition is 'single effort of articulation'. Try saying cat, fat, mate, rack, brief, time, deep etc., you will notice that they require a single chest pulse or a pulse of air pressure (monosyllables). Now say pi.cky, lu.cky, ve.ry, wa.ter, be.tter etc., they require two chest pulses. They're disyllables.
The second part of the definition is '... and forming a word or an element of a word; each of the elements of spoken language comprising a sound of greater sonority (vowel or vowel-equivalent/[vowel-like]) with or without one or more sounds of less sonority (consonants or consonant-equivalents/[less sonorous])'.
In simple words, a syllable must have a vowel/diphthong or a vowel-like sound (Sonorants; /l m n r/ etc). Vowels can make syllables on their own as in eye, oh, awe, ah etc., but non-sonorous consonants can't.
We also have syllabic consonants (Sonorants) such as /l m n/ that can make a syllable on their own. For example, the second syllable in the word rhythm is formed by the syllabic consonant /m/: [rɪ.ðm̩]
Moving on to the original question,
'Brief' is pronounced /briːf/; there's one sonority peak (/iː/) and it requires a single effort of articulation, hence one syllable.
Here's the sonority curve for 'brief':
The blue dot marks the peak of sonority. There's one peak, hence one syllable.
'Client', on the other hand, is questionable. It can be syllabified in different ways, depending on how you pronounce it. Also, vowels in succession can pose a problem.
If its pronounced /ˈklaɪənt/, then it can be transcribed as [ˈclaɪ.jənt] (or [cla.jənt]) because there's often a palatal glide /j/ when one word ends in a front vowel (/i ɪ/) and the next one starts with another vowel. As is the case with /ˈklaɪ.ənt/. That's why it can be transcrbed as [ˈclaɪ.jənt]. Now there are two peaks of sonority; one is formed by /aɪ/ in the first syllable and another by /ə/ in the second syllable. It means 'client' requires two chest pulses/ two efforts of articulation, hence two syllables.
Sonority curtve for 'client':
As you can see, there are two peaks, which means there are two syllables.
'Actual' is usually pronounced /ˈæk.t͡ʃu.əl/. It can be transcribed as [ˈæk.t͡ʃu.wəl] because when one word ends with a rounded vowel (/u ʊ/) and the next one starts with a vowel, there's usually a glide /w/ between both the words. Now there are three peaks, hence three syllables.
Sonority curve for 'actual':
There are three peaks in 'actual'.
Head over to this answer for more details on sonority curves, and to this one for Maximum Onset Principle (how to syllabify words).
(Others might disagree, however.)