If $$x$$ and $$y$$ are real numbers, the least possible value of the expression $$4(x - 2)^{2} + 4(y - 3)^{2} - 2(x - 3)^{2}$$ is :

$$4(x - 2)^{2} + 4(y - 3)^{2} - 2(x - 3)^{2}$$
$$y$$ is an independent variable. The value of $$y$$ is unaffected by the value of $$x$$. Therefore, the least value that the expression $$4(y-3)^2$$ can take is $$0$$ (at $$y=3$$).

Let us expand the remaining terms. 
$$4(x-2)^2-2(x-3)^2$$=4*$$(x^2-4x+4)-2*(x^2-6x+9)$$
$$=2x^2-4x-2$$
=$$2(x^2-2x-1)$$
=$$2(x^2-2x+1-2)$$
=$$2((x-1)^2-2)$$
The least value that the expression $$(x-1)^2$$ can take is $$0$$ (at $$x$$ = $$1$$)
Therefore, the least value that the expression $$2((x-1)^2-2$$ can take is $$2*(0-2)=2*(-2) = -4$$
Therefore, option B is the right answer.