JSX style attributes are similar to HTML style attributes. Both the style attribute and attribute only accept CSS properties. Therefore, the use of selectors, pseudo-elements or pseudo-classes is not allowed.

Using style attributes

Replace the following:

const style = {
    h2 : {
        fontSize: '20px';
        color: 'black';
    } & span: {
       color: 'white';
    }
}

const Main = () => {
    return (
        <h2 style={style}>Hello<span>Test</span></h2> 
   );
}

and:

const h2Style = {
  fontSize: '20px';
  color: 'black';
}
const spanStyle = {
  color: 'white';
}

const Main = () => {
    return (
        <h2 style={h2Style}>Hello<span style={spanStyle}>Test</span></h2> 
   );
}

or clearer:

const styles = {
  h2: {
    fontSize: '20px';
    color: 'black';
  },
  span: {
    color: 'white';
  }
}

const Main = () => {
    return (
        <h2 style={styles.h2}>Hello<span style={styles.span}>Test</span></h2> 
   );
}

However, since you only want to define styles for h2 elements, we have more options:

CSS/SCSS

Using CSS on separate files:

import "./your-css.css";

const Main = () => {
    return (
        <h2 className="title">Hello<span>Test</span></h2> 
   );
}

Among them, the .your-css.css file contains

.title {
  fontSize: '20px';
  color: 'black';
}

.title span {
  color: 'white';
}

Even nested (if you use a preprocessor like .scss)

.title {
  fontSize: '20px';
  color: 'black';

  span {
    color: 'white';
  }
}

CSS-in-JS

Considering a more "React" solution, we could use CSS-in-JS like styled-components Learn more

import React from 'react';
import styled from 'styled-components';

const Title = styled.h2`
  fontSize: '20px';
  color: 'black';

  span {
    color: 'white';
  }
`;

const Main = () => {
    return (
        <Title>Hello<span>Test</span></Title> 
   );
}

export default Main;