dekiru koto wo tsukattekure

dekiru = "to be able to do"
koto = "thing" (conceptual; physical objects are usually "mono" for "thing")

When you apply a verb as a modifier to a noun in Japanese it's similar to when you do it in English. We don't have a single word that has the same meaning as "dekiru", but here's a similar example:

"umareta hito"
umareru = to be born
-ta = past tense
hito = person

This translates to "the person that was born". So as you see, the phrase refers to the thing that is in the state described by the verb. Similarly, "hashitteiru hito" (hashiru = run, -te iru = -ing) means "the person that is running". So "dekiru koto" is "the thing(s) that (you) are able to do". ("You" is implied by the structure of the sentence -- Japanese leaves out pronouns a lot -- and Japanese doesn't change the form of nouns when they're plural so "koto" can be "thing" or "things".)

As for "tsukattekure", it's "tsukau" "to use" in -te form, which is used for connecting verbs together, and "kureru" "to give" in casual imperative (command) form. Literally, it means "use and give", but in this case "kure" is being used idiomatically like "kudasai" (which is the command form of "kudasaru" which ALSO literally means "give" in humble speech) to mean "please". So that's "please use".

Putting it all together, the sentence is "please use the things that you are able to do." Which brings us to the more natural English translation I gave above, "please use what you can."