How can I draw 2,3-diethylheptane?
What I usually do when I start numbering is look for branching and start numbering at the end with the closest branch. Also, keep in mind that with branching you'll want to consider numbering from one of the branches (if it'll yield a long chain.) 

I'm using the structure you made as an example:

Here I numbered from the side with the most branching. But then I numbered it in two different ways. One way was starting with the straight chain which gave me a 7 carbon chain. Then I renumbered it (the image on the right) starting from one of the branches. This gave me an 8 carbon chain. (You could also number starting from the other branch, but that gives you 7 as well.)

Choose the longest chain. Since stuff that looks like a side chain can actually be part of the main chain, seriously keep this in mind during exams. It's totally okay to number the same alkane in different ways and play around with it to find which is the longest chain.

4-ethyl-3-methyloctane



Now, if you're having trouble drawing them:

I would draw just a zig-zag pattern (like I drew above) containing the number of carbons you need. You need a heptane, so start out with a 7 carbon chain.

This will just be your bare, skeleton structure. Then number the carbons, then add the ethyls to carbons 2 and 3.

HOWEVER, the question is flawed. You actually can't have an ethyl on carbon number 2 here, because it just makes the chain longer.