The question is asking for all real values of x for which the two inequalities are true.
As an example, let's try a value of 4 for x. Plugging that value in the first inequality we have
Since 14 is greater than 10 (or not less than 10) our guess of 4 does not belong in the set of all values for which both inequalities are true
Let's try this analytically:
The first inequality is 3x+7<10
Subtracting 7 from both sides we have a new inequality below
3x<3 or x<1
The second inequality is 6x-14>4
Transformations will yield another simplified inequality as shown below
6x>18 or x>3
The x values that hold for both inequalities will be all x values that are common to both x<1 and x>3
Since x cannot be both less than 1 and greater than 3, the solution set is empty.