You haven't shown a top view of the lathe with the countershaft and motor mounted and with the belts in place so we don't know how the 3-step pulley lines up with the 4-step spindle pulley. But the general equation for this case where "P" means "Pulley", "CS" means Countershaft, "*" means "times" or "Multiplied By", "/" means "Divided By", "S" means "Spindle", "1" is the large countershaft pulley, "2" is the in-use step of the CS step pulley and "( )" means to perform the "/" operation between "(" and ")" first before performing the "*" operations.

S-RPM = M-RPM * (M-P-Dia / CS-P1-Dia) * (CS-P2-Dia / S-P-Dia).

Note that the pulley diameters used should be the pitch diameters, not the outside diameters. For an approximation of the pitch diameters, subtract the nominal belt size (probably either 3/8" or 1/2") from the pulley outside diameter. And hopefully there are no typos in the above.