Assimilation happens with sounds that modify each other when they meet, usually across word boundaries, but within words too. If we consider the words that and book, and look at the phonemes involved, we get / ð̠ æ t/ and / b ʊ k /. If we then place the words into a sentence (for example, Could
you pass me that book, please?), we notice that the / t / phoneme at the end of that does not sound like it does in the word said on its own. The phoneme / t / is an alveolar sound which is formed when the tongue blade forms a temporary closure against the alveolar ridge.

If you try saying the sentence a few times over, you will notice that the tongue doesn’t actually get to the alveolar ridge at the end of the word. Rather than having our tongue make the unnecessarily long journey all the way to the alveolar ridge, we employ an economy of effort, and get our articulators (in this case
the lips) ready for the next sound, / b /. The modified sound retains its original voice quality, and so we say that the / t / assimilates to a / p /, both sounds being unvoiced. As a result, we get Could you pass me / ð̠ æ p / / b ʊ k /.
This is not to say that we give the / p / its full plosive manner of articulation either, as we would if we were to say the non-word / ð̠ æ p / on its own, merely that our lips are in the position to make a / p /. The best description is that in readying our articulators for the next sound, certain sounds are either absorbed, or modified into others. There is another possibility: the / t / at the end of that could also become a glottal stop, where the glottis (the opening between the vocal cords – larynx closes momentarily.
Other examples involving the same sounds as the above are:

Can you see that boy over there?
Where has the cat been all night?
Who’s a cute baby, then?

Some rules for assimilation
1 The phonemes / t /, / d / and / n / often become bilabial before bilabial consonants / p /, / b / and / m /:
He’s a rather fat boy. (/ t / assimilates to / p /)
She’s got an apartment in Manhattan. (/ t / assimilates to / p /)
He’s a very good boy. ( / d / assimilates to / b /)
There are ten men in the class, and two women. (/ m / assimilates to / n /)

2 / t / assimilates to / k / before / k / or / g /. / d / assimilates to / g / before / k / or
/ g /:
Where has that cat been all night? (/ t / assimilates to / k /)
Can you see that girl over there? (/ t / assimilates to / k /)
It was a very good concert. (/ d/ assimilates to / g /)
She’s a very good girl. (/ d / assimilates to / g /)

3 / n / can assimilate to / ŋ / before / g / or / k /:
I’ve been_going out too much lately.
He’s bringing his own car.

4 / s / can assimilate to / ʃ / before / ʃ /:
I really love this shiny one over here.

5 / z / can assimilate to / ʒ / before / ʃ /:
We found this lovely little cheese shop in Paris.

The above examples are cases of anticipatory assimilation, where one sound changes to another because of the sound which follows. Here are some cases of coalescent assimilation, where two sounds combine to form a different one:

6 / t / and / j / coalesce to form / tʃ /:
You went to France last year, didn’t you?

7 / d / and / j / coalesce to form / dʒ /:
Would you like a cup of tea?

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