Find the number of integers 1≤x≤210 which are divided by two of the numbers 3,5,7 I went with;
Numbers that can be divided by $3,5$ can also be divided with $15$. These are $15,30,45,60,75,90,105,120,135,150,165,180,195,210$
Numbers that can be divided by $3,7$ can also be divided with $21$. These are $21,42,63,84,105,126,147,168,189$
Numbers that can be divided by $5,7$ can also be divided with $35$. These are 
$35,70,105,140,175,210$
So total number of integers are $14+9+6=$$29$ 
But I'm not sure about my answer.

$$210= 3 \times 5 \times 7 \times 2$$
$$\frac{210}{3 \times 5} = 2 \times 7$$
$$\frac{210}{3 \times 7} = 2 \times 5$$
$$\frac{210}{5 \times 7} = 3 \times 2$$ 
If a number is divisible by all $3$ numbers, it will appear in each list, hence we need to substract $2 \times$ number of multiples of $3 \times 5 \times 7$.
Hence the desired number is 
$$2 \times 7+ 2 \times 5 + 3 \times 2 - 2 \times \frac{210}{3 \times 5 \times 7}=2(7+5+3-2)=26$$
