Two numbers are consecutive integers. six times the smaller integer equals three times the greater integer. find the integers

The integers are 1 and 2. 

Explanation:
Use "x" to represent the smaller integer and "x+1" to represent the larger integer. The whole equation would be 6x=3(x+1). Here's how to solve it:
6x=3(x+1)
6x=3x+3
3x=3
x=1
The smaller integer value is solved. Plug that value into "x+1" to get the larger integer, which will be 2.