Phonics
I think cannot is okay - DS2 sounded it without trouble. Carrot I'm not sure, because the o is schwa, and I don't even know how you cover that in phonics. Similarly begin - I would pronounce the e as schwa confused.
If phonics was as simple as Mrz and co claim, nobody would have any trouble deciding which books can be included in early readers, nor would authors have to take great care to avoid troublesome words.
It's only because English spelling is so messy that many parents, and many young teachers too, are now so unsure about what phonics is and what it isn't. Because SP evangelists now call virtually all teaching of reading and writing phonics, they have made matters much worse than they used to be.
The worst of this is that they have made parents so unsure about how to help with reading, making them worry that they might be doing it wrong. On a one-to-one basis, there is very little that anyone can do wrong in helping a child with learning to read - apart from pushing too hard and getting angry when the child seems to be making little progress.
It's a matter of: sit and listen, encourage the use of decoding as the first approach with unfamiliar words, but just say the word if this is taking too long, keep things moving and keep your cool.
Give a bit more help with very common words that keep causing trouble (e.g. 'trouble). If u take a closer look at those, u will invariably see why they are troublesome - they contain letters with variable sounds (was - wag, swan - swam).
Whatever the phonics brigade claim, the following are very common, but tricky in various ways:
he, of, the, to, was, all, be, are, have, one, said, we, you, call, come, could, do, down, into, me, now, only, other, right, she, some, their, there, two, when, want, were, what, where, which, who, your
and different children will learn them at quite different speeds.