2m + 1
—————— × (9m² - 36)
3m - 6

Write the second part over 1

2m + 1   9m² - 36
—————— × ————————  
3m - 6      1

Factor 3m - 6 as 3(m - 2) 

Factor 9m² - 36 first as 9(m² - 4) and then as
9(m - 2)(m + 2).
               
 2m + 1    9(m - 2)(m + 2)
———————— × ———————————————  
3(m - 2)          1
    
Cancel the 3 factor of the bottom first fraction 
into the 9 factor in the top of the second fraction:

           3   
 2m + 1    9(m - 2)(m + 2)
———————— × ———————————————  
3(m - 2)          1
1   

Now cancel the (m - 2) factor of the bottom first 
fraction into the (m - 2) factor in the top of the 
second fraction:

           3   1
 2m + 1    9(m - 2)(m + 2)
———————— × ———————————————  
3(m - 2)          1
1   1

 2m + 1    3(m + 2)
———————— × ————————  
    1         1

Put parentheses around the 2m + 1 as (2m + 1)

(2m + 1)   3(m + 2)
———————— × ————————  
    1         1

Indicate multiplication of numerators

(2m + 1)3(m + 2)
————————————————
       1

Erase the 1 denominator and just write the numerator

(2m + 1)3(m + 2)

It is preferable to put the shorter factors first:

3(m + 2)(2m + 1)

That is an acceptable answer.  If you like you can
"FOIL" out the two parenthetical binomials:

3(2m² + m + 4m + 2)

then combine the m with the 4m getting 5m

3(2m² + 5m + 2)

then distribute the 3

6m² + 15m + 6

However leaving it in the factored form above 
is just as good.

Edwin
AnlytcPhil@aol.com