When I visited the NYPL several weeks ago, this was one of the 1875 NYS Census records that I found, the record of the Mulvaney Family. It's hard to tell, because the addresses are cut off in the image, but I believe that across the margin is written the word "King" and next to that the number "121." If that's so, it's a couple doors down from 127 King, the address where John Mulvaney was living when his father died in 1885. It's a further few doors away from 135 King, where Bridget Rothwell Mulvaney died in 1883, and a couple blocks from 197 King, where the family was enumerated in 1880. They apparently spent at least a decade just moving up and down the street.
The family is enumerated as James Mulvaney, 48, an Irish-born carpenter and naturalized voter; Bridget, 43, his wife; Thomas, 20; John, 18; Patrick, 15; and Mary A., 13. The children are all Brooklyn-born, and none of them have occupations listed, although 5 years ago, at age 15, Thomas had already been listed as an "Ap. Carpenter." I'd imagine that certainly Thomas and John, and maybe Patrick, were working by this point in time. Looking up the page, however, it seems that only heads of households and other verifiably adult males - men in their 30s and 40s - had their occupations noted. They live in a brick house worth $5,000.