Новая грамматическая тема: конструкции «как ни...» и «сколько ни...» помогают показать, что результат всё равно не меняется.

Here новая грамматическая тема is in the nominative case because it works like a heading or label: New grammar topic: ...

Russian often uses the nominative in this kind of title-like structure before a colon.

• Новая грамматическая тема: ... = A new grammar topic: ...
• It is not the direct object of a verb, so accusative новую грамматическую тему would not fit here.

Also, the adjective and noun agree:

• новая — feminine singular nominative
• грамматическая — feminine singular nominative
• тема — feminine singular nominative

Because the sentence names two constructions:

• как ни...
• сколько ни...

So Russian uses the plural noun конструкции = constructions / patterns.

That is also why the verb is plural:

• конструкции помогают = the constructions help

If there were only one construction, it would be:

• конструкция помогает

This is one of the most important points.

In these patterns, ни is the normal particle, not не. It helps create the meaning of:

• no matter how...
• however...
• no matter how much / how many times...

For example:

• Как ни старайся, ничего не выходит.
  = No matter how hard you try, nothing works out.

• Сколько ни объясняй, он не понимает.
  = No matter how much you explain, he doesn’t understand.

So in these constructions, ни is part of the fixed grammar pattern.

Very roughly:

• не usually negates something directly
• ни often appears in emphatic or concessive patterns like this one

They are similar, but they are used in different kinds of situations.

как ни...

Usually means no matter how... / however... It often refers to manner, degree, or way.

Examples:

• Как ни трудно, надо продолжать.
  = No matter how hard it is, you have to continue.
• Как ни старайся, результат тот же.
  = No matter how hard you try, the result is the same.

сколько ни...

Usually means no matter how much... / no matter how many times... It often refers to quantity, amount, or repeated attempts.

Examples:

• Сколько ни пытался, не смог.
  = No matter how many times he tried, he couldn’t do it.
• Сколько ни читай, всё не запомнишь.
  = No matter how much you read, you still won’t memorize everything.

So:

• как ни... = about how
• сколько ни... = about how much / how many times

Because its subject is конструкции, which is plural.

Russian verbs in the present tense agree with the subject in number:

• конструкция помогает = singular
• конструкции помогают = plural

So in this sentence:

• конструкции помогают показать...
• literally: the constructions help show...

After помогать / помочь, Russian often uses an infinitive to say help do something.

So:

• помогают показать = help show
• помогают понять = help understand
• помогают запомнить = help remember

Here показать is a perfective infinitive. That makes sense because the sentence refers to presenting a complete idea: these constructions help show a specific result or point.

You may also see imperfective infinitives after помогать, depending on context, but показать sounds very natural here.

Всё равно means something like:

• all the same
• anyway
• still
• nevertheless

In this sentence, it emphasizes that the outcome does not change despite the effort or circumstances.

So:

• результат всё равно не меняется = the result still doesn’t change = the result remains the same anyway

This phrase is very common in Russian.

Examples:

• Я устал, но всё равно пойду.
  = I’m tired, but I’ll go anyway.
• Он всё равно не согласится.
  = He still won’t agree / He won’t agree anyway.

Because the subject of that clause is результат, which is singular.

• результат = result
• меняется = changes / is changing

So:

• результат не меняется = the result does not change

If the subject were plural, the verb would also be plural:

• результаты не меняются = the results do not change

Меняться means to change or to be changing, often in the sense of becoming different.

It is the reflexive form related to менять:

• менять = to change something
• меняться = to change / to undergo change

Compare:

• Он меняет план.
  = He changes the plan.
• План меняется.
  = The plan changes / is changing.

So in the sentence:

• результат всё равно не меняется
• the result still does not change

The colon introduces an explanation of what the new grammar topic is.

So the structure is:

• Новая грамматическая тема:
  the new grammar topic is the following

Then the sentence continues by naming the topic:

• конструкции как ни... и сколько ни... помогают...

This is very natural in Russian, especially in textbooks, lessons, slides, and explanations.

Here are a few natural examples.

With как ни...

• Как ни спеши, быстрее не получится.
  = No matter how much you hurry, it won’t go faster.

• Как ни странно, он был прав.
  = Strange as it may seem / No matter how strange it seems, he was right.

• Как ни старайся, всем не угодишь.
  = No matter how hard you try, you can’t please everyone.

With сколько ни...

• Сколько ни звонил, никто не ответил.
  = No matter how many times he called, nobody answered.

• Сколько ни учи, всё забывается.
  = No matter how much you study, everything gets forgotten.

• Сколько ни объясняй, он не слушает.
  = No matter how much you explain, he doesn’t listen.

In all of these, the core idea is the same as in the original sentence: the result stays unchanged despite effort, amount, or repetition.