[tex]10 +\frac{n}{6} = 15\\[/tex]
Let that number be [tex]n[/tex].
The quotient of a number and [tex]6[/tex] is [tex]\frac{n}{6}\\[/tex].
"Increased" is just another term for "plus (+)" so [tex]10[/tex] increased by The quotient of a number and [tex]6[/tex] is [tex]10 + \frac{n}{6}\\[/tex]
And it tells us that it is [tex]15[/tex] so it must be [tex]10 +\frac{n}{6} = 15\\[/tex]