In order to find the value of x in each equation, we will first solve the equations step by step.

1) X-3/6 = 7/9

Multiplying through by 6 to get rid of the denominator:

6(x-3/6) = 6(7/9)
6x - 3 = 42/9
6x - 3 = 14/3

Adding 3 to both sides:

6x = 14/3 + 3
6x = 14/3 + 9/3
6x = 23/3

Dividing by 6:

x = 23/3 * 1/6
x = 23/18

Therefore, x = 23/18.

2) x + 7/3 = 2x + 3/5

Subtracting x from both sides:

7/3 = x + 3/5

Multiplying through by 15 to get rid of the denominators:

157/3 = 15(x) + 153/5
35 = 15x + 9
35 - 9 = 15x
26 = 15x

Dividing by 15:

x = 26/15

Therefore, x = 26/15.