The lines of the form $$a x+b y=c \& a x+b y=c_1$$ are parallel lines $\&$ the distance between them is $$\frac{\left|c-c_1\right|}{\sqrt{a^2+b^2$$ (Note: - Modulus is put as the distance cannot be negative)

The given lines $3$x+4 y=10 \& 6 x+8 y=10$$ i.e. $$3 x+4 y=5$$ are parallel lines, so using the above formula we get the distance between them as $$\frac{|10-5|}{\sqrt{3^2+4^2}$=$\frac{5}{5}$$=1$$

Hence the answer is (B).