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$2^{12}=4096=49^y=7^{2y}=2^{2xy}$ .

Then $12=2xy$ , so $xy=\boxed{6}$ .

From equation $2^x=7\Rightarrow x=\log_27$

From equation $49^y=4096\Rightarrow y=\log_{49}{4096}=\log_{7^2}{2^{12}}=\dfrac{12}2\log_72=6\log_72$

Thus, $xy=(\log_27)(6\log_72)=6(\log_27)\left(\dfrac1{\log_27}\right)=\boxed6$

(log {2}7 ) x (log {49}4096) = 6