Let $N$ be the number of twin numbers that do not exceed $M$. Then $N \ge N_3 + N_4 - N_{12}$, since all the numbers from $M_3$ and $M_4$ are twin, as they have divisors $1, 3$ and $2, 4$ respectively, and $M_2$ consists of all the numbers that belong to both $M_3$ and $M_4$. But there are also twin numbers that do not exceed $M$ and do not belong neither to $M_3$ nor to $M_4$, for example $35 = 5 \cdot 7$, and so we even have that $N > N_3 + N_4 - N_{12}$. Since $M$ is divisible by $12$, we obtain:
$$N > \frac{M}{3} + \frac{M}{4} - \frac{M}{12} = \frac{M}{2},$$
which precisely means that there are more twin numbers than the numbers that are not twin among the first $M = 20112012$ natural numbers.