The question is given to be:
[tex]2q^2-\frac{4}{5}\mleft(5q-6\mright)+4q^2[/tex]
Step 1: Expand the middle term using the Distributive Property given as:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]
Therefore, we get
[tex]\begin{gathered} -\frac{4}{5}(5q-6)=-\frac{4}{5}(5q)-\frac{4}{5}(-6) \\ =-4q+\frac{24}{5} \end{gathered}[/tex]
Thus, the expression becomes:
[tex]\Rightarrow2q^2-4q+\frac{24}{5}+4q^2[/tex]
Step 2: Collect the like terms together.
[tex]\Rightarrow2q^2+4q^2-4q+\frac{24}{5}[/tex]
Step 3: Add and subtract as necessary.
[tex]\Rightarrow6q^2-4q+\frac{24}{5}[/tex]
Step 4: Combine all terms into a single fraction. The lowest common multiple of the 3 terms is 5; this will be the denominator.
[tex]\Rightarrow\frac{5(6q^2)-5(4q)+24}{5}[/tex]
Therefore, we get the answer to be:
[tex]\Rightarrow\frac{30q^2-20q+24}{5}[/tex]
