How come every website I could find is saying that syllables in "photography" are pho-tog-ra-phy? Shouldn't it be pho-to-gra-phy? Where did that "tog" come from?
I'm assuming you are confused by the fact that because we say 'photo' we should then just tack on 'graphy' without changing the pronunciation of 'photo' - so you would arrive at 'photo graphy?
As with many combination words this is not actually true, the emphasis and stressed syllable moves. Similarly with many words suffixed by -ography, -onomy, -ology, the stress moves to the first 'o' of the suffix.
Ge 'og raphy, gastr 'on omy, bi 'ol ogy etc.
This gives us a change from the expected 'photo graphy to conform to this rule and we get pho 'tog raphy. Really the 't' could belong to either group, as you can't stress a consonant in the same way, but a native would perceive 'tog' to be the entire emphasised syllable.
Pho 'to graphy, however, could push the perception back towards our initial misconception of 'photo graphy, with a longer 'o' and so wouldn't convey the correct pronunciation so well.
Using 'tog' [which is a word all of its own, describing the heat retention of clothing, duvets etc] and has a definite short 'o', as in 'hot'. 'To' alone may be perceived as in 'toe', especially as our root word is pronounced 'toe', which leads us astray again.
If you are asking how dictionaries break this into syllables for the purpose of pronunciation, according to several dictionaries, it's pho-to-gra-phy for American English, and your intuition is absolutely correct. In American English, it is only broken into syllables as pho-tog-ra-phy for the purpose of hyphenating the word at the end of the line. In British English, some dictionaries syllabalize it for pronunciation as pho-tog-ra-phy. The difference between these is that the o is "short" or "lax" in British English, meaning it must be followed by a consonant and "long" or "tense" in American English, meaning it need not be followed by a consonant.
These two syllabifications, for pronunciation and hyphenation, don't always agree, although they often do, and you shouldn't use the one of these syllabifications for the purpose of purpose of the other.
See Merriam-Webster Dictionary, that gives the pronunciation (fə-ˈtä-grə-fē) [using its own pronunciation symbols, not IPA]. and Cambridge Dictionary, that gives the American pronunciation /fəˈtɑː.ɡrə.fi/, but the British pronunciation /fəˈtɒɡ.rə.fi/, with the syllable tog, as you were asking about.
Possibly you are asking about how to split the word into syllables so as to hyphenate the word at the end of a line. The rules for hyphenation in English are rather arcane and differ between England and the United States; they usually reflect the pronunciation, but don't always.
Here is a question that gives the rules for hyphenating syllables at the end of a line. I assume that the rule which makes the hyphenation fall after tog is
- Never break a word after a short vowel in an accented syllable (rap-id but stu-pid).
Hyphenating the word after the "o" would be justified by the rule
- Break words at morpheme boundaries.
The vowel in tog is the short vowel /ɒ/ in British English, but is the long vowel /ɑː/ (or sometimes /ɔː/) in American English. However, for purposes of hyphenation, American dictionaries often seem to treat the letter "o" as a short vowel when it's not pronounced /oʊ/. (As I mention above, the rules are arcane.)