For any linear program, we have one of 3 alternatives: it has an optimal solution (opt), it is unbounded (nub), it is infeasible (inf).
The theorem on 4 alternatives gives the following 4 joint alternatives for the program and its dual:

opt 
inf 
unb 
opt 
√ min = max 
 
 
inf 
 
√ 
√ 
unb 
 
√ 
 
where √ means possible and  means impossible.
In the (opt, opt) case, the optimal values for the primal and dual programs are the same.
This outcome (the duality theorem) can be stated as follows: if both programs are feasible, they have optimal solutions and the optimal values are the same.
Another version is: if a linear program has an optimal solution, then the dual program has an optimal solution and the optimal values art the same.