"4 4/9 multiplied by 3/4"
can be written symbolically as (4 4/9)(3/4). The usual approach here is to convert that mixed number, 4 4/9, into an improper fraction: 40/9.
Last, we multiply (40/9) and (3/4) together, obtaining (10)(1/3), or 10/3, or 3 1/3.