I'm trying to say sentences like "I can accomplish (a) by doing (b)." in
Japanese, and I can't seem to figure it out.

An example sentence would be "I can earn good grades by studying hard."

* * *

Maybe the english example wasn't quite right. I know accomplish complicates
the question but I do feel thats what I'm looking for. Maybe this example of
what I'm looking for will help.

"I can show initiative by working hard."

Or if someone was presenting a product demonstration before an audience.

"I can make this product appeal to the audience." "I just need to show its
usefulness."

What I want to construct is more "i can make this product appeal to the
audience by showing its usefulness."

I'm not necessarily looking for a direct translation of these sentences. An
example of how to construct the idea or something similar would work.
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grammar syntax
Sentence structure: "I can accomplish (a) by doing (b)"
I don't think there is a good literal translation of this construction into
Japanese.

Here are some related expressions that might help.

> 「一所懸命{いっしょけんめい}勉強{べんきょう}したら、いい成績{せいせき}を取れる{とれる}。」  
>  "If I study really hard, I can get good grades."
>
> 「一所懸命勉強して、いい成績を取る。」  
>  "I'll study really hard and get good grades."
>
> 「いい成績を取れるように、一所懸命勉強する。」  
>  "I'll study really hard (in order) to get good grades."

Though to be honest, I'm not sure I'd ever say "I can earn good grades by
studying hard." in English, except maybe when literally listing things I could
accomplish by doing something else? If I wanted to do that in Japanese, I
suppose I'd use the first construction I provided: 「〜たら、〜れる。」.

* * *

> "I can show initiative by working hard."

I honestly can't think of a context I'd say this in English. Maybe we speak
different dialects?

> "I can make this product appeal to the audience by showing its usefulness."

I think I would say this when trying to convince someone to entrust a
talk/product to me.

The "can" does not seem particularly core to the meaning, it is more like a
way to commit to less when you say it; compare, "[If you leave it to me] I
will make this product appeal to the audience by showing its usefulness".

For that reason I think it leaves a bad taste in my mouth in English, and I
personally wouldn't say the equivalent of it in Japanese. I would say
something like this:

> 有用性(or実用性/便利さ)を示して、顧客に訴えます。  
>  "I will exhibit its usefulness, and make it appeal to the customers."

(You should wait for a native speaker to check that if you actually want to
say this line to someone, as I'm not particularly good with business
language.)
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You over-complicate your question by putting "accomplish" in there. You should
instead be trying to learn, "if this, then that".

頑張って勉強すると卒業することができます

"If I persevere and study hard, I'll be able to graduate"

You can use と as a conditional linking the former statement to the latter
statement, in a fashion that the former will be IF and the latter will be the
THEN, as in what will happen if the former is true.

To make a similar, but not a 100% concrete certainty statement, you can write
it like

頑張って勉強したら卒業することができます
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There are a number of ways to express this. **Roughly** in the order of
informality, those include:

「～～すれば + Vpotential。」

「～～すれば + Vdictionary + ことができる。」

「～～することで + 《Noun ｜Verb + こと》 + が[可能]{かのう}になる。」

「～～すること《により ｜ によって》 + 《Noun ｜Verb + こと》 + が可能になる。」

「～～すること《により｜によって》 + Noun + が[達成]{たっせい}できる。」

To use one of your examples "I can make this product appeal to the audience by
showing its usefulness.", you can say the following. (I take this to be about
TV shopping.)

「[商品]{しょうひん}の[実用性]{じつようせい}を[示]{しめ}せば、[視聴者]{しちょうしゃ}にアピールできる（or アピールすることができる）。」

「商品の実用性を示すことにより、視聴者 **に** アピールすることが可能になる。」

「商品の実用性 **を** 示すことで、視聴者 **への** アピールが可能になる。」

「商品の実用性 **の** [提示]{ていじ}により、視聴者へのアピールが達成できる。」
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