Here we are given the expression : z+ (z+6)
In this we will use the concept of like terms.
Like terms are terms whose variables (and their exponents such as the 2 in x²) are the same. In other words, terms that are "like" each other.
so here we have z and z which have same exponent which is 1.
So we can say that z and z are like terms.
So adding z and z we get 2z
so our expression becomes 2z+3
Now we may use distributive property here which is :
ab + ac = a(b+c)
where "a" is gcf of the two terms.
so in our expression 2z+6 , gcf is 2
taking 2 common out we have 2(z+3).
So answer is option c) 2(z+3).