How many solutions does the equation have? ?
3(d+11)=6(d+33) m

A powerful way to find out is to solve the equation.  Let's try that.

                         3 (d + 11)  =  6 (d + 33)

Eliminate the parentheses:    3d + 33  =  6d + 198

Subtract  3d  from each side:       33  =  3d + 198

Subtract  198  from each side:     -165 = 3d

Divide each side by  3 :               - 55 = d

There it is ... the solution to the original equation. 
'd' has to be -55, otherwise the original equation isn't a true statement.
-55 is the ONLY number that 'd' can be.  If you write in any other number
for 'd', the equation will be false.

For example, less see what the equation says when  d=2 :

                       3(2 + 11)  =  6(2 + 33)

                       3(  13  )  =  6(  35  )

                           39      =     210

Is that a true statement ?  Is 39 equal to 210 ? 
No.  39 and 210 are not equal.  They are different.
So the equation is not true when d = 2 .
The equation is true ONLY when  d = -55 .

The equation has exactly one solution.