How to figure out how many syllables Голубамголовивідкушувальне has

What's this

It seems that this is a closed compound word, which appears to be a neologism, authors of this show came up on the fly.

This kind of words (Ukr. — голофрастичне утворення/конструкція) is created by lexicalization of syntactic terms.

Notes

• Source: Словотвірні особливості неологізмів у сучасній постмодерністській прозі
• It is worth noting that any Ukrainian speaker will understand this kind of words whatsoever because essentially this is just several words combined in one but it appears that this is something non-natives have trouble with.

Here some examples from the source hereabove (in bold):

1. …гра називається: Мені-зимно-притулись-до-мене-поміцніше (Л. Дереш);
2. Незнаюнезнаюнезнаю (Л. Денисенко);
3. ГосподийдудотебетвояДарцяБорхес (Л. Дереш);

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Unlikely in the real life, though it's still possible, people might just combine words into a one, effectively creating new words, which existence and applicability more likely than not are limited to the context of the ongoing conversation (but this kind of word composition is likely to be encountered in the postmodern fiction books to some degree as outlined above).

This is a case in your scenario.

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Break down and meaning

The original word conforms with the characteristics of an adjective.

Let's outline the words, which form Голубамголовивідкушувальне.

Голубам | голови | відкушувальне

There are three words:

1. Голубам — the word meaning pigeon in the dative plural,
2. голови — the word meaning head in the genitive singular,
3. відкушувальне — the word meaning bite off — відкушувати, which undergone word inflection and appears as an adjective in nominative/accusative (for the word of neuter gender as this one, the nominative and accusative cases match each other) singular.

If we were to change the word order to (subject is not specified):

• відкушувальне голубам голови: verb відкушувальне(in the form of adjective participle)-indirect-object(голубам)-plus-direct-object(голови)-predicate
• відкушувальне голови голубам: verb відкушувальне(in the form of adjective participle)-indirect-object(голови)-plus-direct-object(голубам)-predicate

The meaning becomes rather apparent — something that bites off pigeons' heads.

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Syllables

In Ukrainian, a vowel is a central unit of a syllable meaning a word has the same amount of syllables as there are vowels (source). There are 11 vowels therefore 11 syllables (vowels in bold, the word split into syllables)

го-лу-бам-го-ло-ви-від-ку-шу-ва-льне