Alliteration is used here and there throughout "Afternoon with Irish cows." The first example is in line 1:
There were a few dozen who occupied the field
The /f/ sound is a feature throughout the first stanza, used both in alliteration and consonance within words. This is a gentle, muffled sound that helps build a picture of the soft, turfy Irish grass on which the cows spend their days.
Lines 6 and 7 use the same alliteration, even though the words are quite far apart:
and look out to see the field suddenly empty
as if they had taken wing, flown off to another country
Indeed, even line 9 in the following stanza uses the same alliteration, helping the poem build its opening atmosphere of quiet and calm: "and again the field would be full of their munching." In the first two stanzas, the poem conjures a sense of the mundane—not much happens other than the speaker occasionally seeing cows through a window. The prominent /f/ sound helps lure the reader into this lull, the "long quiet of the afternoon."
The third stanza is the key shift in the poem, breaking the gentle spell of the first two stanzas. Here, a cow lets out a "sound so phenomenal" that it disrupts the speaker's own routine. To match the loud sound made by the cow, the poem turns up its own equivalent volume by featuring more alliteration (as well as assonance and consonance), and making it more varied. In line 16, "sound" and "so" alliterate; in the following line "put" and "paper" create a harsh plosive /p/ sound conveying urgency:
would let out a sound so phenomenal
that I would put down the paper
Elsewhere in the stanza, /s/ consonants keep up this prominent use of poetic sound ("stone," "see," "side," and "spear" all alliterate).
The next key example of alliteration is in lines 27 and 28, the last two lines of the fourth stanza:
that began in the darkness of her belly
and echoed up through her bowed ribs into her gaping mouth.
These lines gather /b/ sounds together in a way that represents the formation of the cow's "full-bodied cry" (which starts in the belly and echoes up through the ribs). It's another plosive sound, requiring the stopping of airflow when read out loud—this makes the alliteration more dramatic and noticeable.
One more example is in lines 34 and 35, the poem's final two lines:
while she regarded my head and shoulders
above the wall with one wild, shocking eye.
These /w/ and /sh/ sounds seem to bring the poem into focus around its closing image—the cow's one staring eye. It helps make the ending more unsettling, with the reversal of perspective landing not just on the speaker, but the reader too.