PANAMA + JAPAN = 5
FIJI + CUBA = 7
SWEDEN + NORWAY = 9
AUSTRIA + AUSTRALIA = 7

Then what is the corresponding value for:

CANADA + UNITED STATES = ?

Let X denote a given word, and let:
n(X) = The total number of distinct letters (of the english alphabet) in X.

In the given problem, for pairs (X,Y) the end result for each given sum is equal to n(X U Y), where X U Y denotes the union between X and Y.

For example, when (X,Y) = (PANAMA, JAPAN), we observe that : n(X U Y) = 5

Now the distinct letters corresponding to XUY, when (X,Y) = (CANADA, UNITED STATES) are: C, A, N, D, U, I, T, E, S giving:
n ('CANADA', 'UNITED STATES') = 9.

Consequently, we must have:
CANADA + UNITED STATES = 9