Answer
$6, +\infty$
Refer to the graph below.
Work Step by Step
$x\ge3$ includes the numbers that are greater than or equal to $3$.
$x\ge6$ includes the numbers that are greater than or equal to $6$.
The conjunction "and" means intersection so find the numbers that are common to both inequalities.
The intersection of the two given sets is the set of real numbers that are greater than or equal to $6$.
Hence, the solution set is $[6, +\infty)$.
Graph the solution set by plotting a solid dot at $6$ then shading the region to its right. (Refer to the graph above.)