Nope, this is easy to visualize dp. It's just you, thinking that everybody here solve problems in their mind, and then code. Nope, it's often hard to solve first problem on topics. So we use pan and paper a lot. I too thought everybody solve in their minds, before I saw top solvers during streams stumble upon some unknown problem, and took out their pen and paper.

For the testcase in poblem dp-table looks like this:

i\j 01234567890
---------------
2   00100000000 
7   00001000001 
6   10002100000
...

You've got first number 2 so we start with this one like this: dp[0][2] = 1

For 7 there is only one 2: (7+2)%10 = 9; (7*2)%10 = 4 => dp[1][9] = 1; dp[1][4] = 1.

Now for 6 there is one 9 and one 4: (6+9)%10 = 5; (6*9)%10 = 4; (6+4)%10 = 0; (6*4)%10 = 4 => so we've got one 5, two 4s and one 0 after 6. => dp[2][0] = 1; dp[2][4] = 1+1; dp[2][5] = 1.

With every new number quantity dobles, but every i-th number is compared (with * and +) only to 10 previous dp[i-1][0...9] (of which nine are zero at begining, so we skip them on paper, but algorithm check them anyway).