A Pythagorean triplets is a triplet which consists of three positive numbers in which the square of one number is equal to the sum of other two numbers such as

a^2+b^2 =c^2

Since,

6^2=36

8^2=64

10^2=100

Therefore,

6^2+8^2=10^2

36+64=100

So the triplet of 6,8,10 is Pythagorean triplets.