Question 5338
Let x = the first consecutive number  
Let x+2 = when two is added to the first consecutive number 

Let x+2 = second even consecutive number 
Let x+4 = when two is added to the second consecutive number

so when multiplied together:
{{{x*(x+2)}}} = {{{x^2+2x}}}

And when multiplied together AFTER 2 has been added to each:
{{{(x+2)*(x+4) = (x^2+6x+8)}}}

the second product is 136 greater than the first
{{{x^2+6x+8=x^2+2x+136}}}
Subtract {{{x^2}}} from both sides:
{{{6x+8=2x+136}}}
Subtract 2x from both sides:
{{{4x+8=136}}}
subtract 8 from both sides:
{{{4x=128}}}
Divide by 4
{{{x=32}}}

So the first number is 32, the second consecutive number is 34.

check your results:
32*34 = 1088
Add two to both numbers:
34*36 = 1224
1224-1088=136