Product means multiplication.

Change the numbers to base 10 and multiply and change it back to base seven.

124_seven = 1 x 7² + 2 x 7¹ + 4 x 7⁰

124_seven = 67

23_seven = 2 x 7¹ + 3 x 7⁰

23_seven = 17

124_seven x 23_seven = 67 x 17

124_seven x 23_seven = 1139

1139 base 10 to base 7

$$\begin{array}{cc}\mathrm{}& 1139\\ 7& \mathrm{162\; r\; 5}\\ 7& \mathrm{23\; r\; 1}\\ 7& \mathrm{3\; r\; 2}\\ 7& \mathrm{0\; r\; 3}\end{array}$$

You list the remainders from the bottom to the top.

1139_ten = 3215_seven