With two blocks hanging from a pulley at opposite ends connected by a block in the middle. What is the tension between the left most block and the middle block?

Tension on the pulley are equal, since they are connected by the same string

So analysing each block

Using Newton law

ΣF = ma

Two forces are acting on the block, the weight and the tension

T-W=ma. Upward

W of the object is given as my

W=mg

T-mg=ma

T=ma+mg

T=m (a+g)

So, this is the tension on the block