help

There is no constant.  Do you mean coefficient?

(6x   +  1 / (3x) )^6

The constant term is

C(6,3)  (6x)³ ( 1 / (3x) )³  =

20 * (6³) (x³) ( 1 / (3³)) ( 1 / x³)  =  

20 * 216 / 27  =  

20 * 8  =  

160

OK......here's another way to solve this

C(6, n) (6x)ⁿ (  1 / (3x) ) ^{6 - n}        and we can write

C (6, n)  ( 6)ⁿ (x)ⁿ  ( 1 / 3)^6-n ( 1 / x) ^6-n

C (6, n)  (6)ⁿ( 1/3)^6-n  ( x)ⁿ  ( 1/x)^6-n

C(6, n) (6)ⁿ (1/3)^6-n ( x)ⁿ  ( x^-1)^6-n

C(6, n)  (6)ⁿ (1/3)^6-n (x)ⁿ ( x)^{n - 6}

C(6, n) (6)ⁿ(1/3)^6-n ( x) ^{2n - 6}

We need to   have    2n - 6  = 0    to eliminate the variable, x

Then   n  must    = 3

So  we have

C(6, 3) (6)³ (1/3)^6-3   

20 * 216 * (1/3)³

20 * 216 *  (1/27)  =

20 * 8  =

160