Given that

$$ f(x)=x^2+7x-3 \ and \ g(x)=x^2-4x+5 $$

and

$$ h(x)=f(x)-g(x) $$

So

$$ h(x)=x^2+7x-3-(x^2-4x+5) $$

$$ h(x)=11x-8 $$

$$ \therefore h(2)=11(2)-8=14 $$