Factorise:

The given expression is $3 y^{2}+14 y+8$

Find two numbers that follow the conditions given below:

Sum $=14$

Product $=24$

Clearly, the numbers are 12 and 2 .

$3 y^{2}+14 y+8=3 y^{2}+12 y+2 y+8$

$=3 y(y+4)+2(y+4)$

$=(3 y+2)(y+4)$