Let a is the first term and r is the common ratio of the GP

Now, given 10th term = 9

=> ar^10-1 = 9

=> ar⁹ = 9 ............1

and given 4th term = 4

=> ar^4-1 = 4

=> ar³ = 4 ............2

Equation 1/equation 2, we get

     ar⁹ /ar³ = 9/4

=> r⁶ = 9/4

Again,

     ar⁹ = 9

=> a*(r³ )³ = 9

=> a*(4/a )³ = 9    {from equation 2}

=> a*64/a³ = 9

=> 64/a² = 9

=> 9a² = 64

=> a² = 64/9

=> a = 8/3

Now, 7th term = ar⁶ = (8/3)*(9/4) = (8*9)/(3*4) = 2*3 = 6