The coefficients of a binomial expansion are determined by the Pascal's triangle.
Take a look at the picture.
draw the Pascal's triangle up to the third row. (the row with only 1 is the zero'th row)
Also, notice that as we expand [tex](A+B) ^{3} [/tex],
in each term the power of A decreases by 1, starting from 3, and the powers of B increase by 1, up to 3.
According to these, the second term of [tex](A+B) ^{3} [/tex] is
[tex]3A^{2}B [/tex],
where A=4x, and B=3y,
substituting A an B:
[tex]3A^{2}B=3(4x)^{2}(3y)=3*16 x^{2} *3y=144 x^{2} y[/tex]
Answer: 144
