To multiply two polynomials together, there are more steps involved than just simple distribution. I like to use the FOIL method, because it is easy to remember and applies to all questions like this one.

FOIL stands for First, Outer, Inner, Last.

"First" means we multiply the first two terms in each of the parentheses:

(x+4)(x+2). "x" times "x" = x^2. This is the first term.

Then, we multiply the Outer numbers.

(x+4)(x+2). "x" times "2" = 2x. This is the second term.

Next, we multiply the Inner terms.

(x+4)(x+2). "4" times "x" = 4x. This is the third term.

Last, we multiply the "last" terms in the parentheses.

(x+4)(x+2). "4" times "2" = 8. This is the last term.

Now we add up all of the terms that we solved for:

x^2 + 2x + 4x +8.

Finally, we simplify like terms by adding them together. 4x and 2x are like terms, so we add them to get 6x.

The final answer is:

x^2 + 6x +8

Please let me know if you need any clarification. I'm always happy to answer your questions.