Hey there! 
To answer this question, suppose that the number is the variable x. 
- "Six more than two times a certain number"
We can represent '6 more than two times a certain number' as: 
2x+6
- "Is less than"
We can represent 'is less than' by using the symbol <
- "The number increased by 20"
Since x is the variable, it would be represented as: 
x+20
So, the final solution is: 
2x+6 < x+20
Thank you!