There is a small issue in this question that is: everybody does not always use the exact same definition of stabilizing selection and disruptive selection. These two concepts are sometimes used to refer to phenotypic traits or to genes. For example stabilizing selection might either mean,
- selection for the mean phenotypic trait of the population
- selection for the wildtype allele, getting rid of all newcoming mutations.
Under simple genetic architecture the two concepts are equal.
Although for this question I don't think we even need to give a clear definitions between these two words, we'll use the phenotypic based definition (the first one above) in order to ease the intuitive understanding of the answer.
Let's say the trait breeders select for is mean quality and for ease again, we'll imagine this trait as being one unique trait that we can map on one axis from low quality to high quality. Here is a representation of that where the x-axis represent meat quality (left = low quality) and the y-axis represents the density of cows in the population which has the associated meat quality.
If breeders performed a stabilizing selection, it means that they would not improve the meat but only prevent the meat to change quality. In order to shift the quality of the meat to the right (to better quality), breeders need to perform directional selection.
I think the only problem that you had for solving this problem was the conceptual issue of considering meat quality just like any phenotypic trait. And if you want to shift a phenotypic trait on one side or another, you have to apply directive selection.