Could someone explain to me how to determine the answer to this question?

Concept: Solution of the given attachment is based on the addition of two vectors as given below.

Consider two vectors P and Q, then resultant of these two vectors is given as,

R = P + Q

To find the addition of G & H vectors. That is G + H =?

In the given figure;

Vector A = - Vector G because both are in opposite directions -----(i)

From the figure,

A + H = F --------------- using the given concept ---------(ii)

Now, shall replace the value of A from equation (i) in equation(ii)

- G + H = F

or, G + (- H) = - F

Since the vector addition of G & H is not equal to F.

Hence, the given statement G + H = F is False.