Question 327097
Let X and Y both be integers, X has two digits. 
{{{171/X=Y+6/X}}}
{{{171=XY+6}}}
{{{XY=165}}}
Look for factors of 165
{{{165=3*5*11}}}
The 2 digit product combiations are then
{{{11}}}
{{{15}}}
{{{33}}}
{{{55}}}
There are 4 2-digit numbers that leave a remainder of 6.
{{{171/11=15+6/11}}}
{{{171/15=11+6/15}}}
{{{171/33=5+6/33}}}
{{{171/55=3+6/55}}}