Question 315423
We have the first equation {{{Y + 12 = S}}} (where Y = yoshi's age, S = her sister's age) 

For the second equation (6 years from now the sum of their ages will equal 32): six years from now we know that Yoshi's age will be Y+6. Her sister's age will be S+6. Thus the equation reads: 
{{{(Y+6) + (S+6) = 32}}}. This is the same as combining like terms to give {{{Y + S + 12 = 32}}} or subtracting 12 from both sides to give {{{Y + S = 20}}}. 

But we know from the first equation that {{{S = Y + 12}}}. Substitute this into {{{Y + S = 20}}} to give {{{Y + (Y+12) = 20}}}. Then combining like terms gives {{{2Y + 12 = 20}}}. Subtracting 12 from both sides gives {{{2Y = 8}}}. Dividing by 2 yields {{{Y = 4}}}. 

Now we check. If yoshi is 4 years old, then his sister is 4+12 = 16 years old. 
In six years, yoshi will be 10. His sister will be 22. The sum of their ages (10 + 22) gives us 32, so the answer yoshi is 4 works.