First of all the product is positive because the product of two negatives is always positive.
Next, we can write the numbers a little differently:
Let's forget about the minus signs because we already know the result has to be positive, and let's just concentrate on the numbers. 2 1/3 is the same as 2+1/3 and 6 1/2 is the same as 6+1/2.
Now we use the distributive property to solve (2+1/3)(6+1/2).
This can be written 2(6+1/2)+(1/3)(6+1/2).
Take each bracket in turn:
2*6+2*1/2=12+1=13; 1/3*6+1/3*1/2=2+1/6.
Now we add these together: 13+2+1/6=15+1/6 or 15 1/6.