The poem is "The Youngest Daughter" by Cathy Song. While the term "syntax" usually refers to the word order of a phrase, clause, or sentence, in Poetry analysis it can refer to the order of thematic development, or the gradual unfolding of metaphorical imagery. For example, in Elizabethan (or Shakespearean) Sonnets, the theme develops in the first lines, then turns to a larger idea, then ends in a rhymed couplet.
In Song's poem, the first stanza describes in the first person some tactile memories of the narrator's mother; the second stanza develops the mutual care of mother and daughter--soothing headaches, giving baths-- the mother's age and health are developed further in Stanza Three (longer, more detailed, adding memories of the past) Stanza Four introduces the possibility that the daughter is trapped by her mother's condition and shows them in repose; The last stanza uses the universal symbol of cranes flying to represent coming death (the soul going to heaven), so we see that the daughter's "imprisonment" will be ended when her mother dieseven though she toasts her mother's health. The poem is a beautiful statement of the tensions between young happy memories and a future life, of the balance between childhood love and a growing desire to start one's own life. Because the narrator is "the youngest daughter, the assumption is that other sisters have cared for the mother, then moved on to their own lives, leaving the youngest daughter to stay with the mother till death frees her. That is the "syntax" of revelations as the poem develops. Because the poem is blank verse, there is little syntactical development in the rhythms of the lines.