Difficulty pronouncing multisyllabic words is a relatively common challenge for children with speech/articulation deficits. While we most often think about speech deficits as a relatively straightforward mispronunciation of specific sounds (such as saying /w/ for /r/ or having a lisp), other conditions, such as a phonological disorder or apraxia of speech, can affect a person's speech in more complex ways. And yes, Broca's area is involved in speech sequencing, but it's more accurate to think about difficulty with multisyllabic words as a broader speech planning or phonological processing network, rather than a single brain region.
Children with articulation difficulties may be able to pronounce a target sound in short, simple words, but mispronounce these sounds in the context of longer, multisyllabic words with increased motor and sequencing demands. You may have experienced something similar when trying to articulate a new phoneme while learning a new language. Perhaps you could pronounce a trilled 'r' in isolation and in short words, but struggled at first to produce that phoneme in 3- or 4-syllable words.
Children with phonological disorders also tend to mispronounce words with relatively consistent mistakes, such as omitting unstressed syllables, reducing consonant clusters to a single phoneme, assimilating phonemes to the same sound (such as saying yeh-yoh for yellow), or confusing similar-sounding phonemes (such as /s/ and /sh/).
Children with apraxia of speech may or may not have the ability to pronounce all phonemes correctly, but have difficulty executing the motor planning needed for speech, which comes into play especially with phonologically complex words and multisyllabic words. Unlike the first two examples, children with apraxia tend to mispronounce the same word in different ways across multiple attempts, and may also have inappropriate stress patterns when speaking.
Adding to all of this, children can sometimes display what are considered idiosyncratic error patterns. These typically are the result of a mispronunciation of a word from a younger developmental state, and the movement pattern for that word (usually common, frequently used words or names) stuck in muscle memory. You'll see this a lot in words like animal, where a child continues to say 'aminal' even though they otherwise have the speech, phonology, and motor planning skills to seemingly be able to pronounce this word.
Given that this difficulty appears frequently for your student and is accompanied by vocabulary concerns, a referral for evaluation by a Speech-Language Pathologist (SLP) would be appropriate. Like most interventions, early intervention is ideal, but your student should still be able to benefit from speech therapy. An evaluation will help determine the best course of action for this student, as the therapy for articulation, phonological deficits, and apraxia all differ. I'm inferring from your school’s name in your email address that it is a private school, and subsequently that there may not be an SLP on campus. Your student should, however, still be able to request an evaluation through their public school district, but their eligibility for services will be more dependent on the state and district frameworks. Another option is pursuing an evaluation and/or services through a private SLP. It's possible that insurance can also help with this cost.
I hope this helps!