Answer
False.
Work Step by Step
The given statement is
$4\sqrt3+5\sqrt3=9\sqrt6$
$4\sqrt3+5\sqrt3$
Use the distributive property.
$(4+5)\sqrt3$
Two radical expressions that have the same indices and the same radicands are called like radicals.
Add like radicals.
$9\sqrt3$
Hence, the given statement is false.