Given that an unchanged sum, the smaller the difference the larger the product. $84=42+42$$$\Rightarrow (2a) \times (3b)=6ab\leqslant {{42}^{2}}\Rightarrow ab\leqslant 294$$. Thus, the largest possible value of $ab$ is $294$. 
Given that $$2a+3b=84$$, the largest possible value of $$a\times b$$ is~\uline{~~~~~~~~~~}~. 

1) $$270$$ 
2) $$272$$ 
3) $$294$$ 
4) $$296$$ 