Here’s a color palette based on your query that includes the specified background, primary, secondary, and tertiary colors, along with additional complementary colors to create a balanced six-color palette.

### Color Palette: **Fresh Serenity**

1. **Background Color: Light Gray**
   - **Name:** Light Gray
   - **Hex Code:** 
                            
                            #f9f9f9
                        
   - **Description:** A soft, neutral background color that provides a calm and modern base for any design.

2. **Primary Color: Mint Green**
   - **Name:** Mint Green
   - **Hex Code:** 
                            
                            #3eb489
                        
   - **Description:** A refreshing and vibrant mint hue that evokes feelings of tranquility and balance.

3. **Secondary Color: Coral**
   - **Name:** Coral
   - **Hex Code:** 
                            
                            #ff6f61
                        
   - **Description:** A warm and inviting coral shade that adds energy and warmth to the palette, perfect for accents.

4. **Tertiary Color: Soft Beige**
   - **Name:** Soft Beige
   - **Hex Code:** 
                            
                            #f5f5dc
                        
   - **Description:** A gentle beige that complements the palette, providing a soft, earthy tone that enhances warmth.

5. **Accent Color: Sky Blue**
   - **Name:** Sky Blue
   - **Hex Code:** 
                            
                            #87ceeb
                        
   - **Description:** A light and airy blue that adds a touch of serenity and can be used to create contrast without overwhelming.

6. **Highlight Color: Peach**
   - **Name:** Peach
   - **Hex Code:** 
                            
                            #ffcc99
                        
   - **Description:** A light peach color that pairs beautifully with the coral and mint green, offering a soft, playful highlight.

### Palette Summary:
This palette, **Fresh Serenity**, combines a soothing background with vibrant and warm colors. The soft gray provides a contemporary canvas, while the mint green and coral create a lively interaction. The addition of soft beige, sky blue, and peach introduces warmth and playfulness, making it ideal for designs that aim to feel fresh, inviting, and balanced.